{ "info": { "id": "ses_f520d514dffeuvK2rSnqu4hevA", "slug": "proud-cactus", "projectID": "global", "directory": "/private/var/folders/t7/b_w5m78j2mbb1ct051p9sv500000gn/T/nudge-opencode-generation-y1E142", "path": "private/var/folders/t7/b_w5m78j2mbb1ct051p9sv500000gn/T/nudge-opencode-generation-y1E142", "title": "Nudge content generation", "agent": "nudge-generation", "model": { "id": "gpt-6-astra", "providerID": "openai", "variant": "low" }, "version": "1.18.30", "summary": { "additions": 0, "deletions": 0, "files": 0 }, "cost": 0, "tokens": { "input": 22944, "output": 1913, "reasoning": 61, "cache": { "read": 30848, "write": 0 } }, "time": { "created": 1789624757938, "updated": 1789624832667 } }, "messages": [ { "info": { "role": "user", "time": { "created": 1789624757956 }, "agent": "nudge-generation", "model": { "providerID": "openai", "modelID": "gpt-6-astra", "variant": "low" }, "system": "You create Codeforces learning content for Nudge. Your job is to understand the best approach for the problem and teach it clearly in your own words, using existing solutions to inform your reasoning.\n\nStart with a brief, targeted web search for existing solutions so relevant editorials are in context before substantial independent problem-solving. Use any supplied tutorial links first; otherwise search by contest ID and problem index. Prefer the official tutorial/editorial, and read relevant explanations rather than relying on search snippets. Look at accessible alternatives when useful, especially if the official explanation is missing, unclear, or unnecessarily complicated. Accepted submissions can also help clarify an approach. Respect supplied source lookup statuses and avoid repeatedly retrying blocked sources. If no usable source is accessible, proceed from the supplied statement.\n\nTreat existing solutions as a starting point, not a constraint. If an approach is clear and suitable, build on it without unnecessary re-derivation. If an explanation has gaps, seems incorrect, or uses a harder method than necessary, reason through it and derive a better or simpler approach when worthwhile. Choose a correct approach that is easy to teach and fits the constraints. Verify it against the supplied statement and edge cases before writing the hints, editorial, and C++ solution.\n\nThe editorial must be self-contained: explain the key insight, algorithm, why it works, complexity, and implementation details a learner needs, filling in steps the source skips. Keep research and verification concise; spend the output on teaching the solution, not narrating the research process. Follow the user prompt and output schema exactly.", "format": { "type": "json_schema", "schema": { "type": "object", "properties": { "status": { "type": "string", "enum": [ "success", "unsolvable" ], "description": "Set to 'success' when the supplied statement defines a solvable programming problem. Set to 'unsolvable' only if the statement is fundamentally incomplete, contradictory, or depends on an inaccessible required resource." }, "reason": { "anyOf": [ { "type": "string", "pattern": "^[^\\u0000]*$", "minLength": 1, "maxLength": 2000 }, { "type": "null" } ], "description": "If status is 'unsolvable', provide a detailed failure message to show users. Name the concrete statement/resource blocker and any relevant source lookup/access status, such as missing official tutorial, 403/Cloudflare challenge, 404, or unavailable accepted submissions. Otherwise null." }, "hints": { "anyOf": [ { "type": "array", "minItems": 5, "maxItems": 5, "description": "Exactly 5 progressive hints, each building on the last.", "items": { "type": "object", "properties": { "order": { "type": "integer", "minimum": 1, "maximum": 5, "description": "Hint number, 1 through 5." }, "content": { "type": "string", "pattern": "^[^\\u0000]*$", "minLength": 1, "maxLength": 10000, "description": "Markdown hint text." } }, "required": [ "order", "content" ], "additionalProperties": false } }, { "type": "null" } ], "description": "If status is 'success', provide exactly 5 progressive hints. Otherwise null." }, "editorial": { "anyOf": [ { "type": "string", "pattern": "^[^\\u0000]*$", "minLength": 1, "maxLength": 100000 }, { "type": "null" } ], "description": "If status is 'success', a prose editorial explaining the solution in Nudge's own voice, with no links, citations, or source/research notes. Otherwise null." }, "solution": { "anyOf": [ { "type": "string", "pattern": "^[^\\u0000]*$", "minLength": 1, "maxLength": 200000 }, { "type": "null" } ], "description": "If status is 'success', a complete C++ solution. Otherwise null." } }, "required": [ "status", "reason", "hints", "editorial", "solution" ], "additionalProperties": false, "title": "problem_response", "description": "Submit the generated content for the problem, or report if it is unsolvable." }, "retryCount": 2 }, "id": "msg_0adf2aec4001kqicd0VcFeSNvP", "sessionID": "ses_f520d514dffeuvK2rSnqu4hevA" }, "parts": [ { "type": "text", "text": "Generate Codeforces learning content: five progressive hints, an original editorial, and AC-quality C++.\n\nFollow the editorial-first research workflow in the system instructions. Use the supplied statement to verify that the source solves this exact problem.\n\nWrite clean Markdown with LaTeX as needed. Use quick and clever humor when appropriate. Tell it like it is (don't sugar-coat responses), and use very casual language. You are fully allowed to swear, just don't overdo it like a sailor (be natural). Deconstruct any false assumptions.\n\nGenerate content for Codeforces problem 2259C: \"101\" (rated 1000).\n\nKnown problem metadata:\n- Contest ID: 2259\n- Index: C\n- Name: 101\n- Rating: 1000 (Codeforces difficulty rating)\n- Tags: constructive algorithms, greedy\n- Problem URL: https://codeforces.com/contest/2259/problem/C\n\nUse the rating and tags as weak signals only. The supplied statement is the source of truth.\n\nProblem Statement:\n\n
C. 101
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

The score of an array $$$b$$$ of length $$$m$$$ is defined as the maximum length of a subarray of $$$b$$$ such that the first and last elements of the subarray are equal to $$$1$$$ and all other elements in the subarray are equal to $$$0$$$. Formally, the score of $$$b$$$ is equal to the maximum integer $$$k$$$ for which there exists an index $$$i$$$ such that:

If there is no subarray meeting the requirements, the score of $$$b$$$ is $$$0$$$.

You are given an array $$$a_1, a_2, \\ldots, a_n$$$, such that each element is equal to one of $$$-1$$$, $$$0$$$, or $$$1$$$. Replace each $$$-1$$$ with either a $$$0$$$ or $$$1$$$ such that the score of $$$a$$$ is maximal over all possible ways to replace the $$$-1$$$s in $$$a$$$.

Input

The first line of each input contains $$$t$$$ ($$$1 \\leq t \\leq 10^4$$$) — the number of test cases.

The first line of each test case contains $$$n$$$ ($$$1 \\leq n \\leq 2 \\cdot 10^5$$$) — the length of $$$a$$$.

The second line of each test case contains $$$a_1, a_2, \\ldots, a_n$$$ ($$$a_i \\in \\{-1, 0, 1\\}$$$) — the array $$$a$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \\cdot 10^5$$$.

Output

For each test case, output $$$n$$$ space separated integers representing $$$a$$$ after the $$$-1$$$s were replaced with $$$0$$$s or $$$1$$$s. If there are multiple possible solutions, output any.

Example
Input
10
6
1 0 -1 0 0 1
7
0 -1 0 0 1 0 1
5
-1 0 0 -1 0
4
0 0 0 0
1
-1
6
1 0 1 0 0 -1
7
0 1 0 0 0 1 0
6
-1 -1 -1 -1 -1 -1
7
-1 0 1 -1 0 0 1
3
-1 0 0
Output
1 0 0 0 0 1\n0 1 0 0 1 0 1\n1 0 0 1 0\n0 0 0 0\n1\n1 0 1 0 0 1\n0 1 0 0 0 1 0\n1 0 0 0 0 1\n0 0 1 0 0 0 1\n1 0 0
Note

In the first test case, we can change the only $$$-1$$$ to a $$$0$$$, making $$$a = [1, 0, 0, 0, 0, 1]$$$. Since the first and last elements of $$$a$$$ are equal to $$$1$$$, and all other elements are $$$0$$$, the score of $$$a$$$ is $$$6$$$.

In the third test case, changing both $$$-1$$$s to $$$1$$$s makes $$$a = [1, 0, 0, 1, 0]$$$, and the largest subarray that satisfies the conditions in the statement is from the $$$1$$$-st index to the $$$4$$$-th index.

In the fifth test case, we set the only $$$-1$$$ to $$$1$$$, making $$$a = [1]$$$, meaning the largest subarray that satisfies the conditions in the statement is the full array.

\n\n\n\nSource lookup status:\n\n- Tutorial (en): https://codeforces.com/blog/entry/156457 loaded (200 OK; title: \"Codeforces Round 1119 (Div. 3) Editorial - Codeforces\"; mentions 2259C)\n\n\nGenerate:\n1. Five progressive hints, from a gentle nudge to the key insight.\n2. A self-contained editorial that teaches the solution clearly, including the key insight, algorithm, correctness argument, complexity, and necessary implementation details. Explain non-obvious steps without padding or a discovery-process transcript.\n3. A complete C++26 solution that gets AC on Codeforces.\n\nFormatting & Style Rules:\n- Hints and editorial: valid Markdown with LaTeX as needed (e.g., $dp[i]$, $$\\sum_{i=1}^{n} a_i$$).\n- Hints and editorial must read like Nudge's own explanation. No research notes, source notes, citations, Markdown links, URLs, or references to editorials/submissions/posts.\n- Solution: raw C++ only, no Markdown fences.\n- Keep C++ short, clean, standard, and single-file. Comments are fine when they clarify the idea.\n\nOutput strictness:\n- Return JSON matching the provided schema exactly.\n- Never include NUL (U+0000) characters in any field. Use literal $ or $$ for math delimiters, never control characters.\n- If the problem is solvable, return `status: \"success\"`, `reason: null`, and fill in `hints`, `editorial`, and `solution`.\n- Return `status: \"unsolvable\"`, a short `reason`, and set `hints`, `editorial`, and `solution` to null only when the supplied statement is fundamentally incomplete, contradictory, or dependent on an inaccessible resource needed to define the task. Missing research, high rating, uncertainty, or \"can't guarantee AC\" is not a reason to return unsolvable.\n- If you return `status: \"unsolvable\"`, the `reason` is shown directly to users. Be concrete: say what exact statement/resource blocker stopped you, and include relevant source lookup status if it mattered (for example: official tutorial missing, Codeforces returned 403/Cloudflare challenge, tutorial page 404, accepted submissions unavailable).\n- Each hint must be an object with `order` (1 through 5) and `content` (the Markdown hint text), not a plain string. The `content` must contain just the hint text, with no \"Hint 1:\" or subtitles. The UI adds those automatically.\n- Do not start the editorial with an \"# Editorial\" heading. The UI already adds that section. Feel free to add other headers as needed though.\n- Use styling in the editorial if needed! Just that first header is no good but any subheaders or bolding or whatever is good!\n\nFor the C++ solution, you MUST use this template and work around it:\n\n```cpp\n#include \nusing namespace std;\n\nusing ll = long long;\n\nvoid setIO() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n}\n\nint main() {\n setIO();\n}\n```", "id": "prt_0adf2aec5001K57EgLLX1umjcq", "sessionID": "ses_f520d514dffeuvK2rSnqu4hevA", "messageID": "msg_0adf2aec4001kqicd0VcFeSNvP" } ] }, { "info": { "parentID": "msg_0adf2aec4001kqicd0VcFeSNvP", "role": "assistant", "mode": "nudge-generation", "agent": "nudge-generation", "variant": "low", "path": { "cwd": "/private/var/folders/t7/b_w5m78j2mbb1ct051p9sv500000gn/T/nudge-opencode-generation-y1E142", "root": "/" }, "cost": 0, "tokens": { "total": 9225, "input": 9193, "output": 32, "reasoning": 0, "cache": { "write": 0, "read": 0 } }, "modelID": "gpt-6-astra", "providerID": "openai", "time": { "created": 1789624758080, "completed": 1789624766150 }, "finish": "tool-calls", "id": "msg_0adf2af40001VKzA3MerMdhx7p", "sessionID": "ses_f520d514dffeuvK2rSnqu4hevA" }, "parts": [ { "type": "step-start", "id": "prt_0adf2b8c60011tXz1c1ic8VepG", "sessionID": "ses_f520d514dffeuvK2rSnqu4hevA", "messageID": "msg_0adf2af40001VKzA3MerMdhx7p" }, { "type": "tool", "tool": "webfetch", "callID": "call_bmMCXo5hpcodGshDVUOwgFni", "state": { "status": "completed", "input": { "url": "https://codeforces.com/blog/entry/156457", "format": "markdown" }, "output": "---\nimage: https://codeforces.com/codeforces.org/s/21069/images/codeforces-telegram-square-1024x1024.png\ntitle: Codeforces Round 1119 (Div. 3) Editorial - Codeforces\ndescription: Codeforces. Programming competitions and contests, programming community\n---\n\n \n\n \n[![Codeforces](//codeforces.com/codeforces.org/s/21069/images/codeforces-logo-with-telegram-555x130.png \"Codeforces\")](https://codeforces.com/) \n\n[![In English](//codeforces.com/codeforces.org/s/21069/images/flags/24/gb.png \"In English\")](https://codeforces.com/blog/entry/156457?locale=en) [![По-русски](//codeforces.com/codeforces.org/s/21069/images/flags/24/ru.png \"По-русски\")](https://codeforces.com/blog/entry/156457?locale=ru) \n\n[Enter](https://codeforces.com/enter?back=%2Fblog%2Fentry%2F156457)| [Register](https://codeforces.com/register) \n\n \n* [Home](https://codeforces.com/)\n* [Top](https://codeforces.com/top)\n* [Catalog](https://codeforces.com/catalog)\n* [Contests](https://codeforces.com/contests)\n* [Gym](https://codeforces.com/gyms)\n* [Problemset](https://codeforces.com/problemset)\n* [Groups](https://codeforces.com/groups)\n* [Rating](https://codeforces.com/ratings)\n* 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![Text created or updated](//codeforces.com/codeforces.org/s/21069/images/icons/x-update-12x12.png \"Text created or updated\")\n* [kondasujay2](https://codeforces.com/profile/kondasujay2 \"International Master kondasujay2\") → [Codeforces Round 1120 (Div 1, Div 2) Editorial](https://codeforces.com/blog/entry/156688) ![Text created or updated](//codeforces.com/codeforces.org/s/21069/images/icons/x-update-12x12.png \"Text created or updated\")\n* [adarshsolanki2004](https://codeforces.com/profile/adarshsolanki2004 \"Newbie adarshsolanki2004\") → [Cloudflare anti-bot verification not appearing](https://codeforces.com/blog/entry/151688) ![New comment\\(s\\)](//codeforces.com/codeforces.org/s/21069/images/icons/comment-12x12.png \"New comment(s)\")\n* [123gjweq2](https://codeforces.com/profile/123gjweq2 \"Master 123gjweq2\") → [Is this a good problem + can you please help me gauge its difficulty?](https://codeforces.com/blog/entry/156760) ![Text created or updated](//codeforces.com/codeforces.org/s/21069/images/icons/x-update-12x12.png \"Text created or updated\")\n\n| | [Detailed →](https://codeforces.com/recent-actions) |\n| | --------------------------------------------------- |\n\n* [nik\\_exists](https://codeforces.com/profile/nik%5Fexists)\n* [Blog](https://codeforces.com/blog/nik%5Fexists)\n* [Teams](https://codeforces.com/teams/with/nik%5Fexists)\n* [Submissions](https://codeforces.com/submissions/nik%5Fexists)\n* [Groups](https://codeforces.com/groups/with/nik%5Fexists)\n* [Contests](https://codeforces.com/contests/with/nik%5Fexists)\n* [Problemsetting](https://codeforces.com/contests/writer/nik%5Fexists)\n\n### [nik\\_exists's blog](https://codeforces.com/blog/nik%5Fexists)\n\n[ Codeforces Round 1119 (Div. 3) Editorial ](https://codeforces.com/blog/entry/156457) \n\nBy [nik\\_exists](https://codeforces.com/profile/nik%5Fexists \"Expert nik_exists\"), 12 days ago, ![In English](//codeforces.com/codeforces.org/s/21069/images/flags/24/gb.png \"In English\") \n\nThank y'all so much for participating!\n\n[2259A - Moo Language School](https://codeforces.com/contest/2259/problem/A \"Codeforces Round 1119 (Div. 3)\")\n\n**Solution**\n\nTutorial is loading...\n\n**Code**\n\n```\n#include \nusing namespace std;\n\nint main() {\n int t;\n cin >> t;\n\n while (t--) {\n int n, k;\n cin >> n >> k;\n\n string s;\n cin >> s;\n\n int ans = 0;\n for (int i = 0; i < n / k; i++) {\n bool has_non_nhoj_farm = false;\n for (int j = i * k; j < (i + 1) * k; j++) {\n if (s[j] == '0') has_non_nhoj_farm = true;\n }\n ans += !has_non_nhoj_farm;\n }\n\n cout << ans << \"\\n\";\n }\n}\n\n```\n\n**Difficulty**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too hard\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") A bit on the harder side\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good difficulty\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Easy\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too easy\n\n**Quality**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Amazing\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") So-so\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Bad\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Awful\n\n[2259B - Minus Two](https://codeforces.com/contest/2259/problem/B \"Codeforces Round 1119 (Div. 3)\")\n\n**Hint 1**\n\nWhen comparing two numbers that are initially not equal, the only way they can become equal after some number of operations is if at least one of them has an operation performed on it when it is $$$ \\\\lt 2$$$.\n\n**Hint 2**\n\nIf two elements are equal at some point, they'll be equal no matter how many more operations are performed. Therefore, it suffices to look at the end behavior of each element.\n\n**Solution**\n\nTutorial is loading...\n\n**Code**\n\n```\n#include \nusing namespace std;\n \nint main() {\n int t;\n cin >> t;\n \n while (t--) {\n int n;\n cin >> n;\n \n vector vec(n); for (auto &x: vec) cin >> x;\n \n int mod_4[] {0, 0, 0, 0};\n for (auto &x: vec) mod_4[x%4]++;\n cout << max({mod_4[0], mod_4[2], mod_4[1] + mod_4[3]}) << \"\\n\";\n }\n}\n\n```\n\n**Difficulty**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too hard\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") A bit on the harder side\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good difficulty\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Easy\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too easy\n\n**Quality**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Amazing\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") So-so\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Bad\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Awful\n\n[2259C - 101](https://codeforces.com/contest/2259/problem/C \"Codeforces Round 1119 (Div. 3)\")\n\n**Hint 1**\n\nIf a $$$-1$$$ is in between two $$$1$$$s, it would only hurt the answer to make it a $$$1$$$.\n\n**Hint 2**\n\nIf a $$$-1$$$ is not in between two $$$1$$$ s, the $$$-1$$$ would only be included in a subarray satisfying the conditions if it was an endpoint.\n\n**Solution**\n\nTutorial is loading...\n\n**Code**\n\n```\n#include \nusing namespace std;\n \nint main() {\n int t;\n cin >> t;\n \n while (t--) {\n int n;\n cin >> n;\n \n vector vec(n); for (auto &x: vec) cin >> x;\n \n for (int i = 0; i < n; i++) {\n if (vec[i] == -1) vec[i] = 1;\n if (vec[i] == 1) break;\n }\n \n for (int i = n-1; i >= 0; i--) {\n if (vec[i] == -1) vec[i] = 1;\n if (vec[i] == 1) break;\n }\n \n \n for (auto &x: vec) cout << max(x, 0) << \" \";\n cout << \"\\n\";\n }\n}\n\n```\n\n**Difficulty**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too hard\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") A bit on the harder side\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good difficulty\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Easy\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too easy\n\n**Quality**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Amazing\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") So-so\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Bad\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Awful\n\n[2259D - MEX Multiset](https://codeforces.com/contest/2259/problem/D \"Codeforces Round 1119 (Div. 3)\")\n\n**Hint 1**\n\nIf there is only one $$$0$$$ in the array, then exactly one set will have a mex greater than zero\n\n**Hint 2**\n\n$$$MEX(A) = MEX(B), MEX(C) = 0$$$ satisfies the constraints.\n\n**Solution**\n\nTutorial is loading...\n\n**Code**\n\n```\n#include \nusing namespace std;\n \nint main() {\n int t;\n cin >> t;\n \n while (t--) {\n int n;\n cin >> n;\n \n vector vec(n); for (auto &x: vec) cin >> x;\n if (count(vec.begin(), vec.end(), 0) == 1) {\n cout << \"NO\\n\";\n continue;\n }\n cout << \"YES\\n\";\n bool seen_zero = false;\n for (int i = 0; i < n; i++) {\n if (vec[i] != 0) cout << 'A';\n else if (seen_zero) cout << 'B';\n else {\n seen_zero = true;\n cout << 'C';\n }\n }\n cout << \"\\n\";\n }\n}\n\n```\n\n**Difficulty**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too hard\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") A bit on the harder side\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good difficulty\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Easy\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too easy\n\n**Quality**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Amazing\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") So-so\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Bad\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Awful\n\n[2259E - Treasure Map Destruction (Constructive Version)](https://codeforces.com/contest/2259/problem/E \"Codeforces Round 1119 (Div. 3)\")\n\n**Hint 1**\n\nIf an element $$$x$$$ at index $$$i$$$ is not equal to $$$-1$$$, there must be a treasure at either island $$$i + x$$$ or $$$i - x$$$\n\n**Hint 2**\n\nIf an element $$$x$$$ at index $$$i$$$ is not equal to $$$-1$$$, there must no treasures in the exclusive range of indices ($$$i + x$$$, $$$i - x$$$)\n\n**Solution**\n\nTutorial is loading...\n\n**Code**\n\n```\n#include \nusing namespace std;\n#define ll long long\n \nint main() {\n int t;\n cin >> t;\n \n \n while (t--) {\n int n;\n cin >> n;\n \n vector vec(n); for (auto &x: vec) cin >> x;\n \n vector diff(n+1);\n for (int i = 0; i < n; i++) {\n if (vec[i] > 0) {\n diff[max(0, i-vec[i]+1)]++; \n diff[min(n, i+vec[i])]--; \n }\n }\n vector restricted(n);\n int curr_count = 0;\n for (int i = 0; i < n; i++) {\n curr_count += diff[i];\n restricted[i] = curr_count > 0;\n }\n bool possible = true;\n for (int i = 0; i < n && possible; i++) {\n if (vec[i] >= 0) {\n if (i - vec[i] >= 0 && !restricted[i - vec[i]]) continue;\n if (i + vec[i] < n && !restricted[i + vec[i]]) continue;\n possible = false;\n }\n }\n \n if (!possible) cout << -1 << \"\\n\";\n else {\n for (auto x: restricted) cout << !x;\n cout << \"\\n\";\n } \n }\n}\n\n```\n\n**Difficulty**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too hard\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") A bit on the harder side\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good difficulty\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Easy\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too easy\n\n**Quality**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Amazing\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") So-so\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Bad\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Awful\n\n[2259F - Binary Bubble Sort Inversions](https://codeforces.com/contest/2259/problem/F \"Codeforces Round 1119 (Div. 3)\")\n\n**Hint 1**\n\nLook at performing some bubbles and reverse bubbles on small arrays. How many elements are moved?\n\n**Hint 2**\n\nA bubble will result is the leftmost 1 being moved all the way to the right. Similarly, a reverse bubble will result in the rightmost 0 being moved all the way to the left.\n\n**Hint 3**\n\nSince prefix zeroes and suffix ones don't matter, if we continuously remove them, then a bubble removes the last element of the array and a reverse bubble removes the first element of the array. Is there a way to remove the first and last elements of an array in constant time?\n\n**Solution**\n\nTutorial is loading...\n\n**Code**\n\n```\n#include \nusing namespace std;\n \n#define ll long long\nint main() {\n int t;\n cin >> t;\n \n while (t--) {\n int n;\n cin >> n;\n \n vector vec(n); for (auto &x: vec) cin >> x;\n string s;\n cin >> s;\n \n ll inversions = 0;\n int cnt_ones = 0;\n for (int i = 0; i < n; i++) {\n cnt_ones += vec[i];\n if (vec[i] == 0) inversions += cnt_ones;\n }\n cout << inversions << \" \";\n \n deque dq;\n for (auto &x: vec) dq.push_back(x);\n int cnt_zeroes = count(vec.begin(), vec.end(), 0);\n for (int i = 0; i < n; i++) {\n while (dq.size() > 0 && dq.front() == 0) {\n dq.pop_front();\n cnt_zeroes--;\n }\n while (dq.size() > 0 && dq.back() == 1) dq.pop_back();\n if (dq.size() == 0) {\n cout << 0 << \" \";\n continue;\n }\n if (s[i] == '0') {\n inversions -= (dq.size() - cnt_zeroes);\n dq.pop_back();\n cnt_zeroes--;\n }\n else {\n inversions -= cnt_zeroes;\n dq.pop_front();\n }\n cout << inversions << \" \";\n }\n cout << \"\\n\";\n }\n}\n\n```\n\n**Difficulty**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too hard\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") A bit on the harder side\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good difficulty\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Easy\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too easy\n\n**Quality**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Amazing\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") So-so\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Bad\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Awful\n\n[2259G - Index Removal](https://codeforces.com/contest/2259/problem/G \"Codeforces Round 1119 (Div. 3)\") \n\n**Hint 1**\n\nIgnoring indexes 1 and $$$n$$$, if we remove index $$$i$$$, if we perform an operation on index $$$j$$$, all elements between $$$\\[i, j\\]$$$ will also have an operation performed on them.\n\n**Hint 2**\n\nIf we remove index $$$i$$$, and we have to reduce the element at index $$$i+1$$$, $$$i+2$$$, etc, what will we subtract it to?\n\n**Solution**\n\nTutorial is loading...\n\n**Code**\n\n```\n#include \nusing namespace std;\n \n#define ll long long\nint main() {\n int t;\n cin >> t;\n \n while (t--) {\n ll n, k;\n cin >> n >> k;\n \n vector vec(n); for (auto &x: vec) cin >> x;\n vector vec_2(n); for (int i = 0; i < n; i++) vec_2[i] = vec[i] - i * k;\n \n vector prefix(n); prefix[0] = vec[0];\n for (int i = 1; i < n; i++) prefix[i] = prefix[i-1] + vec[i];\n \n vector ans(n);\n for (int i = 1; i < n-1; i++) {\n int lo = i+1;\n int hi = n-1;\n while (lo <= hi) {\n int mid = lo + (hi - lo) / 2;\n if (vec_2[mid] <= (vec[i-1] - i*k)) hi = mid - 1;\n else lo = mid + 1;\n }\n \n ll num_needed = (lo - i - 1);\n ans[i] = (prefix[num_needed + i] - prefix[i]) - (k * (num_needed * (num_needed + 1))/2) - vec[i-1] * num_needed;\n }\n for (auto &x: ans) cout << x << \" \";\n cout << \"\\n\";\n }\n}\n\n```\n\n**Difficulty**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too hard\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") A bit on the harder side\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good difficulty\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Easy\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too easy\n\n**Quality**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Amazing\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") So-so\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Bad\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Awful\n\n[2259H - Treasure Map Destruction (Counting Version)](https://codeforces.com/contest/2259/problem/H \"Codeforces Round 1119 (Div. 3)\")\n\nRead the solution to problem E first\n\n**Hint 1**\n\nLet's consider all locations that we have not restricted: we can separate them into 3 categories: the position is forced to be a treasure, the position has no undestroyed that depend on it, and all other positions. \n\n**Hint 2**\n\nThe islands that are considered \"non-restricted\" form a chain of locations, with each non-restricted chain having a treasure between them. What must be true of the locations in this chain such that no condition is violated?\n\n**Hint 3**\n\nFor every pair of adjacent locations, there must be at least one treasure at one of those locations.\n\n**Solution**\n\nTutorial is loading...\n\n**Code**\n\n```\n#include \nusing namespace std;\n#define ll long long\n \nconst ll MOD = 1000000007;\nconst int MAX_N = 200055;\nint main() {\n int t;\n cin >> t;\n \n \n vector fibo(MAX_N);\n fibo[1] = 1;\n fibo[2] = 1;\n for (int i = 3; i < MAX_N; i++) {\n fibo[i] = (fibo[i-1] + fibo[i-2]) % MOD;\n }\n \n while (t--) {\n int n;\n cin >> n;\n \n vector vec(n); for (auto &x: vec) cin >> x;\n \n vector diff(n+1);\n for (int i = 0; i < n; i++) {\n if (vec[i] > 0) {\n diff[max(0, i-vec[i]+1)]++; \n diff[min(n, i+vec[i])]--; \n }\n }\n \n vector restricted(n);\n vector forced(n);\n vector non_required;\n int curr_count = 0;\n for (int i = 0; i < n; i++) {\n curr_count += diff[i];\n restricted[i] = curr_count > 0;\n }\n \n bool possible = true;\n for (int i = 0; i < n; i++) {\n if (vec[i] != -1) {\n int cnt = 0;\n cnt += (i - vec[i] >= 0 && !restricted[i - vec[i]]); \n cnt += (i + vec[i] < n && !restricted[i + vec[i]]);\n if (cnt == 0) { possible = false;}\n if (cnt == 1 || vec[i] == 0) {\n if (i + vec[i] < n) forced[i + vec[i]] = true;\n if (i - vec[i] >= 0) forced[i - vec[i]] = true;\n }\n }\n }\n for (int i = 0; i < n; i++) {\n if (!restricted[i] && !forced[i]) non_required.push_back(i);\n }\n if (!possible) {\n cout << 0 << \"\\n\";\n continue;\n }\n \n ll total = 1;\n int chain_len = 1;\n for (int i = 0; i < non_required.size(); i++) {\n bool cond1 = i == non_required.size() - 1 || vec[(non_required[i] + non_required[i+1])/2] == (non_required[i+1] - non_required[i])/2;\n bool cond2 = i == non_required.size() - 1 || (non_required[i+1] - non_required[i]) % 2 == 0;\n //if (i != 1) cout << (non_required[i+1] - non_required[i]) << \"\\n\";\n if (i == non_required.size() - 1 || !cond1 || !cond2) {\n //cout << chain_len << \"\\n\";\n total *= fibo[chain_len+2];\n total %= MOD;\n chain_len = 1;\n }\n else chain_len++;\n }\n if (count(vec.begin(), vec.end(), -1) == n) {\n total = (total + MOD - 1) % MOD;\n }\n cout << total << \"\\n\";\n }\n}\n\n```\n\n**Difficulty**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too hard\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") A bit on the harder side\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good difficulty\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Easy\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Too easy\n\n**Quality**\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Amazing\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Good\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") So-so\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Bad\n\n[ ](https://codeforces.com/data/like?action=like \"I like this\") Awful\n\n![](//codeforces.com/codeforces.org/s/21069/images/icons/paperclip-16x16.png) Tutorial of [Codeforces Round 1119 (Div. 3)](https://codeforces.com/contest/2259) \n\n* [![Vote: I like it](//codeforces.com/codeforces.org/s/21069/images/actions/voteup-gray.png \"Vote: I like it\")](#)\n* +202\n* [![Vote: I do not like it](//codeforces.com/codeforces.org/s/21069/images/actions/votedown-gray.png \"Vote: I do not like it\")](#)\n\n* [![Author](//codeforces.com/codeforces.org/s/21069/images/blog/user_16x16.png \"Author\")](https://codeforces.com/profile/nik%5Fexists) [nik\\_exists ](https://codeforces.com/profile/nik%5Fexists)\n* ![Publication date](//codeforces.com/codeforces.org/s/21069/images/blog/date_16x16.png \"Publication date\") 12 days ago\n* [![Comments](//codeforces.com/codeforces.org/s/21069/images/blog/comments_16x16.png \"Comments\")](https://codeforces.com/blog/entry/156457#comments) [118 ](https://codeforces.com/blog/entry/156457#comments)\n\n \n![Comments](//codeforces.com/codeforces.org/s/21069/images/icons/comments-48x48.png \"Comments\") Comments (118) \n\n[Write comment?](#) \n\n| » [nik\\_exists](https://codeforces.com/profile/nik%5Fexists \"Expert nik_exists\") | 12 days ago, [show (+1)](#) # |\n| -------------------------------------------------------------------------------- | ----------------------------- |\n\n| » [ ![](https://codeforces.com/userpic.codeforces.org/no-avatar.jpg) ](https://codeforces.com/profile/nik%5Fexists) [nik\\_exists](https://codeforces.com/profile/nik%5Fexists \"Expert nik_exists\") | 12 days ago, [hide](#) [#](https://codeforces.com/blog/entry/156457?#comment-1390585 \"Link to comment\") \\| [![Vote: I like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-voteup-blue.png \"Vote: I like it\")](#) +8 [![Vote: I do not like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-votedown-blue.png \"Vote: I do not like it\")](#) _Auto comment: topic has been updated by [nik\\_exists](https://codeforces.com/profile/nik%5Fexists \"Expert nikexists\") ([previous revision](https://codeforces.com/topic/157099/en2), [new revision](https://codeforces.com/topic/157099/en3), [compare](https://codeforces.com/topic/157099/diff/en2/en3))._ [→](#) [Reply](#) |\n| -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |\n\n* | » » [wbw121124](https://codeforces.com/profile/wbw121124 \"Specialist wbw121124\") | 11 days ago, [show (+1)](#) # |\n| -------------------------------------------------------------------------------- | ----------------------------- |\n\n| » » [ ![](https://codeforces.com/userpic.codeforces.org/3260004/avatar/bfc5f8da6bb8c097.jpg) ](https://codeforces.com/profile/wbw121124) [wbw121124](https://codeforces.com/profile/wbw121124 \"Specialist wbw121124\") | 11 days ago, [hide](#) [#](https://codeforces.com/blog/entry/156457?#comment-1390753 \"Link to comment\") [^](#comment-1390585 \"Parent comment\") \\| [![Vote: I like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-voteup-blue.png \"Vote: I like it\")](#) +3 [![Vote: I do not like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-votedown-blue.png \"Vote: I do not like it\")](#) where are codesit only have cpp [→](#) [Reply](#) |\n| --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |\n\n * | » » » [knkttp](https://codeforces.com/profile/knkttp \"Specialist knkttp\") | 11 days ago, [show](#) # |\n| ------------------------------------------------------------------------- | ------------------------ |\n\n| » » » [ ![](https://codeforces.com/userpic.codeforces.org/5193194/avatar/1319107b0a053e8e.jpg) ](https://codeforces.com/profile/knkttp) [knkttp](https://codeforces.com/profile/knkttp \"Specialist knkttp\") | 11 days ago, [hide](#) [#](https://codeforces.com/blog/entry/156457?#comment-1390760 \"Link to comment\") [^](#comment-1390753 \"Parent comment\") \\| [![Vote: I like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-voteup-blue.png \"Vote: I like it\")](#) 0 [![Vote: I do not like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-votedown-blue.png \"Vote: I do not like it\")](#) Wait until the hack end [→](#) [Reply](#) |\n| ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |\n * | » » » [nik\\_exists](https://codeforces.com/profile/nik%5Fexists \"Expert nik_exists\") | 10 days ago, [show (+1)](#) # |\n| ------------------------------------------------------------------------------------ | ----------------------------- |\n\n| » » » [ ![](https://codeforces.com/userpic.codeforces.org/no-avatar.jpg) ](https://codeforces.com/profile/nik%5Fexists) [nik\\_exists](https://codeforces.com/profile/nik%5Fexists \"Expert nik_exists\") | 10 days ago, [hide](#) [#](https://codeforces.com/blog/entry/156457?#comment-1390952 \"Link to comment\") [^](#comment-1390753 \"Parent comment\") \\| [![Vote: I like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-voteup-blue.png \"Vote: I like it\")](#) 0 [![Vote: I do not like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-votedown-blue.png \"Vote: I do not like it\")](#) Code has been added! [→](#) [Reply](#) |\n| ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |\n\n * | » » » » [wbw121124](https://codeforces.com/profile/wbw121124 \"Specialist wbw121124\") | 10 days ago, [show](#) # |\n| ------------------------------------------------------------------------------------ | ------------------------ |\n\n| » » » » [ ![](https://codeforces.com/userpic.codeforces.org/3260004/avatar/bfc5f8da6bb8c097.jpg) ](https://codeforces.com/profile/wbw121124) [wbw121124](https://codeforces.com/profile/wbw121124 \"Specialist wbw121124\") | 10 days ago, [hide](#) [#](https://codeforces.com/blog/entry/156457?#comment-1391001 \"Link to comment\") [^](#comment-1390952 \"Parent comment\") \\| [![Vote: I like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-voteup-blue.png \"Vote: I like it\")](#) 0 [![Vote: I do not like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-votedown-blue.png \"Vote: I do not like it\")](#) OK [→](#) [Reply](#) |\n| ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |\n\n| » [furqansuleymanli](https://codeforces.com/profile/furqansuleymanli \"Newbie furqansuleymanli\") | 12 days ago, [show (+1)](#) # |\n| ----------------------------------------------------------------------------------------------- | ----------------------------- |\n\n| » [ ![](https://codeforces.com/userpic.codeforces.org/5563911/avatar/f4984ba07dcb9e51.jpg) ](https://codeforces.com/profile/furqansuleymanli) [furqansuleymanli](https://codeforces.com/profile/furqansuleymanli \"Newbie furqansuleymanli\") | 12 days ago, [hide](#) [#](https://codeforces.com/blog/entry/156457?#comment-1390593 \"Link to comment\") \\| [![Vote: I like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-voteup-blue.png \"Vote: I like it\")](#) +2 [![Vote: I do not like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-votedown-blue.png \"Vote: I do not like it\")](#) good contest! [→](#) [Reply](#) |\n| ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |\n\n* | » » [nik\\_exists](https://codeforces.com/profile/nik%5Fexists \"Expert nik_exists\") | 12 days ago, [show](#) # |\n| ---------------------------------------------------------------------------------- | ------------------------ |\n\n| » » [ ![](https://codeforces.com/userpic.codeforces.org/no-avatar.jpg) ](https://codeforces.com/profile/nik%5Fexists) [nik\\_exists](https://codeforces.com/profile/nik%5Fexists \"Expert nik_exists\") | 12 days ago, [hide](#) [#](https://codeforces.com/blog/entry/156457?#comment-1390642 \"Link to comment\") [^](#comment-1390593 \"Parent comment\") \\| [![Vote: I like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-voteup-blue.png \"Vote: I like it\")](#) +7 [![Vote: I do not like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-votedown-blue.png \"Vote: I do not like it\")](#) tysm! [→](#) [Reply](#) |\n| ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ |\n* | » » [dhiruuu\\_singh26](https://codeforces.com/profile/dhiruuu%5Fsingh26 \"Newbie dhiruuu_singh26\") | 11 days ago, [show](#) # |\n| ------------------------------------------------------------------------------------------------- | ------------------------ |\n\n| » » [ ![](https://codeforces.com/userpic.codeforces.org/4933574/avatar/bca47b478c630dee.jpg) ](https://codeforces.com/profile/dhiruuu%5Fsingh26) [dhiruuu\\_singh26](https://codeforces.com/profile/dhiruuu%5Fsingh26 \"Newbie dhiruuu_singh26\") | 11 days ago, [hide](#) [#](https://codeforces.com/blog/entry/156457?#comment-1390883 \"Link to comment\") [^](#comment-1390593 \"Parent comment\") \\| [![Vote: I like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-voteup-blue.png \"Vote: I like it\")](#) 0 [![Vote: I do not like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-votedown-blue.png \"Vote: I do not like it\")](#) TIGER! TIGER!........ [→](#) [Reply](#) |\n| ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |\n* | » » [While.1](https://codeforces.com/profile/While.1 \"Newbie While.1\") | 10 days ago, [show](#) # |\n| ---------------------------------------------------------------------- | ------------------------ |\n\n| » » [ ![](https://codeforces.com/userpic.codeforces.org/5072827/avatar/578ea0266e326443.jpg) ](https://codeforces.com/profile/While.1) [While.1](https://codeforces.com/profile/While.1 \"Newbie While.1\") | 10 days ago, [hide](#) [#](https://codeforces.com/blog/entry/156457?#comment-1390954 \"Link to comment\") [^](#comment-1390593 \"Parent comment\") \\| [![Vote: I like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-voteup-blue.png \"Vote: I like it\")](#) 0 [![Vote: I do not like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-votedown-blue.png \"Vote: I do not like it\")](#) felt that problem F was more trickier than problem G! [→](#) [Reply](#) |\n| --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |\n\n| » [why127pan](https://codeforces.com/profile/why127pan \"Newbie why127pan\") | 12 days ago, [show (+1)](#) # |\n| -------------------------------------------------------------------------- | ----------------------------- |\n\n| » [ ![](https://codeforces.com/userpic.codeforces.org/5327650/avatar/5df2e47dfbff541b.jpg) ](https://codeforces.com/profile/why127pan) [why127pan](https://codeforces.com/profile/why127pan \"Newbie why127pan\") | 12 days ago, [hide](#) [#](https://codeforces.com/blog/entry/156457?#comment-1390594 \"Link to comment\") \\| [![Vote: I like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-voteup-blue.png \"Vote: I like it\")](#) 0 [![Vote: I do not like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-votedown-blue.png \"Vote: I do not like it\")](#) nice round thanks ! [→](#) [Reply](#) |\n| --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |\n\n* | » » [nik\\_exists](https://codeforces.com/profile/nik%5Fexists \"Expert nik_exists\") | 12 days ago, [show](#) # |\n| ---------------------------------------------------------------------------------- | ------------------------ |\n\n| » » [ ![](https://codeforces.com/userpic.codeforces.org/no-avatar.jpg) ](https://codeforces.com/profile/nik%5Fexists) [nik\\_exists](https://codeforces.com/profile/nik%5Fexists \"Expert nik_exists\") | 12 days ago, [hide](#) [#](https://codeforces.com/blog/entry/156457?#comment-1390645 \"Link to comment\") [^](#comment-1390594 \"Parent comment\") \\| [![Vote: I like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-voteup-blue.png \"Vote: I like it\")](#) +6 [![Vote: I do not like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-votedown-blue.png \"Vote: I do not like it\")](#) tysm! [→](#) [Reply](#) |\n| ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ |\n\n| » [megahertz13](https://codeforces.com/profile/megahertz13 \"Pupil megahertz13\") | 12 days ago, [show (+1)](#) # |\n| ------------------------------------------------------------------------------- | ----------------------------- |\n\n| » [ ![](https://codeforces.com/userpic.codeforces.org/2827759/avatar/2d153e90dd0538bd.jpg) ](https://codeforces.com/profile/megahertz13) [megahertz13](https://codeforces.com/profile/megahertz13 \"Pupil megahertz13\") | 12 days ago, [hide](#) [#](https://codeforces.com/blog/entry/156457?#comment-1390596 \"Link to comment\") \\| [![Vote: I like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-voteup-blue.png \"Vote: I like it\")](#) 0 [![Vote: I do not like it](//codeforces.com/codeforces.org/s/21069/images/actions/comment-votedown-blue.png \"Vote: I do not like it\")](#) good problems, C was kind of annoying to implement [→](#) [Reply](#) |\n\n...201282 bytes truncated...\n\nThe tool call succeeded but the output was truncated. Full output saved to: /Users/zayd/.local/share/opencode/tool-output/tool_0adf2cebe001QSXWDsNhWn8jfr\nUse the Task tool to have explore agent process this file with Grep and Read (with offset/limit). Do NOT read the full file yourself - delegate to save context.", "metadata": { "truncated": true, "outputPath": "/Users/zayd/.local/share/opencode/tool-output/tool_0adf2cebe001QSXWDsNhWn8jfr" }, "title": "https://codeforces.com/blog/entry/156457 (text/markdown; charset=utf-8)", "time": { "start": 1789624761434, "end": 1789624766144 } }, "metadata": { "openai": { "itemId": "fc_06d7c7c2581688a9016aab81b87b1087d2a9bac1bfc43d3853" } }, "id": "prt_0adf2b8c8001J6Iccuj05bMa2W", "sessionID": "ses_f520d514dffeuvK2rSnqu4hevA", "messageID": "msg_0adf2af40001VKzA3MerMdhx7p" }, { "reason": "tool-calls", "type": "step-finish", "tokens": { "total": 9225, "input": 9193, "output": 32, "reasoning": 0, "cache": { "write": 0, "read": 0 } }, "cost": 0, "id": "prt_0adf2cec3001AL4m0jM3voz4t0", "sessionID": "ses_f520d514dffeuvK2rSnqu4hevA", "messageID": "msg_0adf2af40001VKzA3MerMdhx7p" } ] }, { "info": { "parentID": "msg_0adf2aec4001kqicd0VcFeSNvP", "role": "assistant", "mode": "nudge-generation", "agent": "nudge-generation", "variant": "low", "path": { "cwd": "/private/var/folders/t7/b_w5m78j2mbb1ct051p9sv500000gn/T/nudge-opencode-generation-y1E142", "root": "/" }, "cost": 0, "tokens": { "total": 22453, "input": 13166, "output": 266, "reasoning": 61, "cache": { "write": 0, "read": 8960 } }, "modelID": "gpt-6-astra", "providerID": "openai", "time": { "created": 1789624766153, "completed": 1789624778261 }, "finish": "tool-calls", "id": "msg_0adf2cec90019JFX8IYH44uPFm", "sessionID": "ses_f520d514dffeuvK2rSnqu4hevA" }, "parts": [ { "type": "step-start", "id": "prt_0adf2d74d001FWIlkDRhU4h4Nf", "sessionID": "ses_f520d514dffeuvK2rSnqu4hevA", "messageID": "msg_0adf2cec90019JFX8IYH44uPFm" }, { "type": "reasoning", "text": "**Formalizing regional bounds**", "time": { "start": 1789624768334, "end": 1789624772433 }, "metadata": { "openai": { "itemId": "rs_0c6c6dbc6a6a6a59016aab81c03d6087d1ace3ec6f24e5e403", "reasoningEncryptedContent": "gAAAAABqq4HDvMgdQgNxzwsjxXQR6GcyAs1gQNlzqAo3qq1K5ri9ziSvZMSNVRw0rtdWTm1JOkQVYGu0JrHP2_cTGPeKp6WSCN8ltXcnkicdTHhTiZK41xN09FLFjysQRAX40eEg6mSB3iTlUKk2GBoc1GH1SHQs2O3ofFov0mDP_396Ds2DFJiwkinIuydPYqpeSTVY-XJSF9aItWcmS636KNwv7yKdj4jtWUb7Tv4e5E_GXkd28RqecI5cDJlAGpeOskSn6nqiUyLqUrZlIqtlN7XYM4i8YdA8YIEOk9Uyo0oH0hf_6UT9ImsK46pR9GET5h3l3AkwqBdJ5MqzWy9K9idASy9UQWa7TYajYyw12FR8mcOaff1WkMVm5Inxw6CzPriobR4cMdkQA3ok5WH5H__8Abi3A0iVGbfShzp_n7HAV1zolN5evQFncKfL8BYp9mG3LDgzMElkyE__n3_MuyLcPR2OUnUMFTR0uNU_VSTtYvFLNGjytN0EsZGNiK0Wd2V4yxDHPYeovuZMRwdh6FwM_e50hMU6Gyy9oNVPsPN8fztC0E5Is_qEN-_dNwBQ2IreePg84EqIEH1XkSm1jWYNvORHTXD_G1NIz3ytksAjEC4xPYYidXTAwacPmxQg3XoocLcPXgnmde7XCaRC9ga5QA2HSYBMKmBoYGItji1VvD-87QWY2v0DDU0U0LUT3Oo0BTKceHgSwgoYK3Z7aoRiA8AMTp3PNgxmG-4di72lilgKiol-JbcScgJg8JJfeg3BRJdAgEw1QG_EqoGF1HuoRnRDKdS_HsgsmWIXH_vEueQI9P-DdS9BuUxLqvokvg1nCFF389gPc9K4GqwQOf7MxNIKekyMSdqHAxdwEPHZlAqSzW_xw7WqY3KDunkZ25j1fbyC79DYXpUncTvzl9z_13mZHvC2ciNkCyXv4ClPvBWilurBgPOr2ABasUQD7zbVEEVaGc3jaDiLt5JxZU6KzhFyHcjwVimRwtbOGotVL-29wPnsU-x9rd5yuJPaRBx7aLnVK-K-lk3HubqtZgvIa2q_Zp4wu7U7LpRljT9heEVMrLR1SM2xC-6URtPk9zAaaw-v-T6RJTVhF1Fx3sRUjDPmlNqAEZ7jMJ4ElaWyppQG7lEB4nXQFVN-UTijMnePGa8io-WQzPyxMHOFDra7LYe5jnvZlP3F-Uydz1Eknev6pqikgXuSyt9oDECvzclM6sjLgvrZYlbKZu25zM1T8WrGfZ9G2pqDYPmmOFkV8NJqEkJLAByH_iiDYkqQHRyImCqB5x-3olKEg8DaE8BWK9Q_4937pLWO-qBVN_pA-iTOKYira5nXQeERhFDcJBc_1KqkozyhEbnUBUCB0AX2_iXmTwY5HYBxWa6jygajv0QdX3KFA4mmOszqenxKMnW7rHw0fe9WaBysW-QARumHH74k_7MGK3LqjO7oYDjL2RjX_-hFFbX8-Ga8E9unFzNP4-n0yTl1QMEJWpOzCzmWgxTGuVQlOUpK2TZGO1doj1_1Apdo15Nh3CTAfQ5QS5UCKgdMJ0yoi9ovwKf4QzUuilOy-qq0T2dHn873XMSfqygkKOznDDJBMHpTVcG_fhTXf8mtaoHLr5If0nWgWviaWPrX1PPbFEfv0Ta7pYouKLNMWAPZZ7ovWN4aPso24LD6Bd-C3B8BS06_PpKYGogA57Jehgu1SBt6TSLZrroAptlchcw=" } }, "id": "prt_0adf2d74e001GZcYwZD26L10ut", "sessionID": "ses_f520d514dffeuvK2rSnqu4hevA", "messageID": "msg_0adf2cec90019JFX8IYH44uPFm" }, { "type": "tool", "tool": "bash", "callID": "call_72RUHSxf1jxHYEfcWYaW3h6L", "state": { "status": "completed", "input": { "command": "python3 -c 'from itertools import product\n\ndef score(a):\n p=[i for i,x in enumerate(a) if x==1]\n return max([1 if p else 0]+[y-x+1 for x,y in zip(p,p[1:])])\n\ncount=0\nfor n in range(1,9):\n for a in product((-1,0,1),repeat=n):\n p=[i for i,x in enumerate(a) if x!=0]\n b=[max(x,0) for x in a]\n if p: b[p[0]]=b[p[-1]]=1\n unknown=[i for i,x in enumerate(a) if x==-1]\n best=0\n for values in product((0,1),repeat=len(unknown)):\n c=list(a)\n for i,x in zip(unknown,values): c[i]=x\n best=max(best,score(c))\n assert score(b)==best,(a,b,best)\n count+=1\nprint(\"Verified\",count,\"arrays against all replacements\")'", "timeout": 120000 }, "output": "Verified 9840 arrays against all replacements\n", "metadata": { "output": "Verified 9840 arrays against all replacements\n", "exit": 0, "truncated": false }, "title": "python3 -c 'from itertools import product\n\ndef score(a):\n p=[i for i,x in enumerate(a) if x==1]\n return max([1 if p else 0]+[y-x+1 for x,y in zip(p,p[1:])])\n\ncount=0\nfor n in range(1,9):\n for a in product((-1,0,1),repeat=n):\n p=[i for i,x in enumerate(a) if x!=0]\n b=[max(x,0) for x in a]\n if p: b[p[0]]=b[p[-1]]=1\n unknown=[i for i,x in enumerate(a) if x==-1]\n best=0\n for values in product((0,1),repeat=len(unknown)):\n c=list(a)\n for i,x in zip(unknown,values): c[i]=x\n best=max(best,score(c))\n assert score(b)==best,(a,b,best)\n count+=1\nprint(\"Verified\",count,\"arrays against all replacements\")'", "time": { "start": 1789624778124, "end": 1789624778259 } }, "metadata": { "openai": { "itemId": "fc_0c6c6dbc6a6a6a59016aab81c3f7fc87d1a56cabcb6a806967" } }, "id": "prt_0adf2e75f001SQv73pb2dP9gRH", "sessionID": "ses_f520d514dffeuvK2rSnqu4hevA", "messageID": "msg_0adf2cec90019JFX8IYH44uPFm" }, { "reason": "tool-calls", "type": "step-finish", "tokens": { "total": 22453, "input": 13166, "output": 266, "reasoning": 61, "cache": { "write": 0, "read": 8960 } }, "cost": 0, "id": "prt_0adf2fe14001HB2C0Qmepvqkr2", "sessionID": "ses_f520d514dffeuvK2rSnqu4hevA", "messageID": "msg_0adf2cec90019JFX8IYH44uPFm" } ] }, { "info": { "parentID": "msg_0adf2aec4001kqicd0VcFeSNvP", "role": "assistant", "mode": "nudge-generation", "agent": "nudge-generation", "variant": "low", "path": { "cwd": "/private/var/folders/t7/b_w5m78j2mbb1ct051p9sv500000gn/T/nudge-opencode-generation-y1E142", "root": "/" }, "cost": 0, "tokens": { "total": 24088, "input": 585, "output": 1615, "reasoning": 0, "cache": { "write": 0, "read": 21888 } }, "modelID": "gpt-6-astra", "providerID": "openai", "time": { "created": 1789624778262, "completed": 1789624832663 }, "finish": "tool-calls", "structured": { "status": "success", "reason": null, "hints": [ { "order": 1, "content": "Focus on one scoring subarray. Its endpoints must be able to become $1$, and its interior cannot contain an original $1$. Also, a single $1$ counts as a valid subarray of length $1$." }, { "order": 2, "content": "Original $1$s are permanent barriers: a valid subarray cannot cross one in its interior. Between two consecutive original $1$s, what happens if you turn every $-1$ into $0$?" }, { "order": 3, "content": "Between consecutive original $1$s, making every unknown $0$ gives the longest possible subarray in that region. Before the first original $1$, choose the leftmost possible endpoint; after the last original $1$, choose the rightmost possible endpoint." }, { "order": 4, "content": "If there are no original $1$s, use the leftmost and rightmost $-1$ as endpoints and make all other unknowns $0$. If there is only one $-1$, those endpoints are the same position—and that's fine." }, { "order": 5, "content": "All cases collapse into one construction: find the first and last positions whose original values are not $0$, set those positions to $1$, and replace every remaining $-1$ with $0$. Keep all original $1$s. If the array is all zeros, leave it alone. No score calculation is needed." } ], "editorial": "The trick is that we don't need to find which subarray wins. We can make every relevant region as good as possible at the same time.\n\n### What blocks a long scoring subarray?\n\nA valid subarray has $1$s at its endpoints and only $0$s strictly between them. A single $1$ is also valid, with length $1$; adjacent $1$s give length $2$.\n\nTwo observations drive the construction:\n\n- An original $0$ cannot be an endpoint.\n- An original $1$ cannot lie strictly inside a valid subarray. It's a permanent barrier.\n\nAdding more $1$s isn't automatically helpful. Inside a promising gap, an extra $1$ just chops it into smaller pieces.\n\n### Build all the best gaps at once\n\nSuppose the original $1$s occur at positions $p_1 Find the first and last positions whose values are not $0$. Set both to $1$, then replace every remaining $-1$ with $0$.\n\nThese positions are exactly the outermost places where a $1$ is possible. If either is already $1$, it stays unchanged. All other original $1$s also stay unchanged.\n\n### Algorithm\n\nFor each test case:\n\n1. Read the array and find its first and last nonzero positions, $L$ and $R$. Here, “nonzero” includes both $-1$ and $1$.\n2. If these positions exist, set $a_L=a_R=1$.\n3. Replace every remaining $-1$ with $0$.\n4. Output the array.\n\nFor example,\n\n$$[-1,0,1,-1,0,0,1] \\longrightarrow [1,0,1,0,0,0,1].$$\n\nThe original $1$s remain barriers, and the gap between them reaches length $5$. The extra $1$ on the far left doesn't interfere with that gap.\n\n### Why this is optimal\n\nFirst, the construction is legal: it never changes an original $0$ or $1$, and every unknown becomes either $0$ or $1$.\n\nNow consider any valid subarray in any possible completion.\n\n**Case 1: there are no original $1$s.**\n\nIf the array is all zeros, every completion has score $0$. Otherwise, every possible endpoint lies between $L$ and $R$, so no valid subarray can have length greater than $R-L+1$. Our construction makes exactly $[L,R]$ valid, including when $L=R$.\n\n**Case 2: there is at least one original $1$.**\n\nSince a valid subarray cannot contain an original $1$ strictly inside it, it must be contained in one of these regions:\n\n- $[L,p_1]$;\n- $[p_i,p_{i+1}]$ for some consecutive original $1$s;\n- $[p_k,R]$.\n\nOur construction makes every one of these regions a valid subarray: each has endpoints equal to $1$ and only zeros inside. Therefore, any valid subarray from any other completion is no longer than a valid region in our completion.\n\nSo no other completion can achieve a larger score. The construction is optimal.\n\n### Complexity and implementation details\n\nFinding the endpoints and producing the answer take $O(n)$ time per test case. The array uses $O(n)$ memory, with $O(1)$ additional working space.\n\nFind $L$ and $R$ **before** replacing unknowns with zeros. Use a sentinel such as $L=-1$ for an all-zero array. Setting the endpoints also works when $L=R$, so the single-element cases need no special branch.", "solution": "#include \nusing namespace std;\n\nusing ll = long long;\n\nvoid setIO() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n}\n\nint main() {\n setIO();\n\n int t;\n cin >> t;\n while (t--) {\n int n;\n cin >> n;\n vector a(n);\n int L = -1, R = -1;\n\n for (int i = 0; i < n; ++i) {\n cin >> a[i];\n if (a[i] != 0) {\n if (L == -1) L = i;\n R = i;\n }\n }\n\n if (L != -1) a[L] = a[R] = 1;\n\n for (int i = 0; i < n; ++i) {\n if (a[i] == -1) a[i] = 0;\n cout << a[i] << (i + 1 == n ? '\\n' : ' ');\n }\n }\n}\n" }, "id": "msg_0adf2fe16001uJKXQFdSU2ZAsi", "sessionID": "ses_f520d514dffeuvK2rSnqu4hevA" }, "parts": [ { "type": "step-start", "id": "prt_0adf31471001rxi9vkJu4GMFbB", "sessionID": "ses_f520d514dffeuvK2rSnqu4hevA", "messageID": "msg_0adf2fe16001uJKXQFdSU2ZAsi" }, { "type": "tool", "tool": "StructuredOutput", "callID": "call_d8txmBVnrNRMxkhupAqqzsQj", "state": { "status": "completed", "input": { "status": "success", "reason": null, "hints": [ { "order": 1, "content": "Focus on one scoring subarray. Its endpoints must be able to become $1$, and its interior cannot contain an original $1$. Also, a single $1$ counts as a valid subarray of length $1$." }, { "order": 2, "content": "Original $1$s are permanent barriers: a valid subarray cannot cross one in its interior. Between two consecutive original $1$s, what happens if you turn every $-1$ into $0$?" }, { "order": 3, "content": "Between consecutive original $1$s, making every unknown $0$ gives the longest possible subarray in that region. Before the first original $1$, choose the leftmost possible endpoint; after the last original $1$, choose the rightmost possible endpoint." }, { "order": 4, "content": "If there are no original $1$s, use the leftmost and rightmost $-1$ as endpoints and make all other unknowns $0$. If there is only one $-1$, those endpoints are the same position—and that's fine." }, { "order": 5, "content": "All cases collapse into one construction: find the first and last positions whose original values are not $0$, set those positions to $1$, and replace every remaining $-1$ with $0$. Keep all original $1$s. If the array is all zeros, leave it alone. No score calculation is needed." } ], "editorial": "The trick is that we don't need to find which subarray wins. We can make every relevant region as good as possible at the same time.\n\n### What blocks a long scoring subarray?\n\nA valid subarray has $1$s at its endpoints and only $0$s strictly between them. A single $1$ is also valid, with length $1$; adjacent $1$s give length $2$.\n\nTwo observations drive the construction:\n\n- An original $0$ cannot be an endpoint.\n- An original $1$ cannot lie strictly inside a valid subarray. It's a permanent barrier.\n\nAdding more $1$s isn't automatically helpful. Inside a promising gap, an extra $1$ just chops it into smaller pieces.\n\n### Build all the best gaps at once\n\nSuppose the original $1$s occur at positions $p_1 Find the first and last positions whose values are not $0$. Set both to $1$, then replace every remaining $-1$ with $0$.\n\nThese positions are exactly the outermost places where a $1$ is possible. If either is already $1$, it stays unchanged. All other original $1$s also stay unchanged.\n\n### Algorithm\n\nFor each test case:\n\n1. Read the array and find its first and last nonzero positions, $L$ and $R$. Here, “nonzero” includes both $-1$ and $1$.\n2. If these positions exist, set $a_L=a_R=1$.\n3. Replace every remaining $-1$ with $0$.\n4. Output the array.\n\nFor example,\n\n$$[-1,0,1,-1,0,0,1] \\longrightarrow [1,0,1,0,0,0,1].$$\n\nThe original $1$s remain barriers, and the gap between them reaches length $5$. The extra $1$ on the far left doesn't interfere with that gap.\n\n### Why this is optimal\n\nFirst, the construction is legal: it never changes an original $0$ or $1$, and every unknown becomes either $0$ or $1$.\n\nNow consider any valid subarray in any possible completion.\n\n**Case 1: there are no original $1$s.**\n\nIf the array is all zeros, every completion has score $0$. Otherwise, every possible endpoint lies between $L$ and $R$, so no valid subarray can have length greater than $R-L+1$. Our construction makes exactly $[L,R]$ valid, including when $L=R$.\n\n**Case 2: there is at least one original $1$.**\n\nSince a valid subarray cannot contain an original $1$ strictly inside it, it must be contained in one of these regions:\n\n- $[L,p_1]$;\n- $[p_i,p_{i+1}]$ for some consecutive original $1$s;\n- $[p_k,R]$.\n\nOur construction makes every one of these regions a valid subarray: each has endpoints equal to $1$ and only zeros inside. Therefore, any valid subarray from any other completion is no longer than a valid region in our completion.\n\nSo no other completion can achieve a larger score. The construction is optimal.\n\n### Complexity and implementation details\n\nFinding the endpoints and producing the answer take $O(n)$ time per test case. The array uses $O(n)$ memory, with $O(1)$ additional working space.\n\nFind $L$ and $R$ **before** replacing unknowns with zeros. Use a sentinel such as $L=-1$ for an all-zero array. Setting the endpoints also works when $L=R$, so the single-element cases need no special branch.", "solution": "#include \nusing namespace std;\n\nusing ll = long long;\n\nvoid setIO() {\n ios::sync_with_stdio(false);\n cin.tie(nullptr);\n}\n\nint main() {\n setIO();\n\n int t;\n cin >> t;\n while (t--) {\n int n;\n cin >> n;\n vector a(n);\n int L = -1, R = -1;\n\n for (int i = 0; i < n; ++i) {\n cin >> a[i];\n if (a[i] != 0) {\n if (L == -1) L = i;\n R = i;\n }\n }\n\n if (L != -1) a[L] = a[R] = 1;\n\n for (int i = 0; i < n; ++i) {\n if (a[i] == -1) a[i] = 0;\n cout << a[i] << (i + 1 == n ? '\\n' : ' ');\n }\n }\n}\n" }, "output": "Structured output captured successfully.", "metadata": { "valid": true }, "title": "Structured Output", "time": { "start": 1789624832553, "end": 1789624832556 } }, "metadata": { "openai": { "itemId": "fc_028e0acb8c5d3bfd016aab81cfee3887d19bb4609c7d4410ec" } }, "id": "prt_0adf31473001xs6vAaHl3BHGp7", "sessionID": "ses_f520d514dffeuvK2rSnqu4hevA", "messageID": "msg_0adf2fe16001uJKXQFdSU2ZAsi" }, { "reason": "tool-calls", "type": "step-finish", "tokens": { "total": 24088, "input": 585, "output": 1615, "reasoning": 0, "cache": { "write": 0, "read": 21888 } }, "cost": 0, "id": "prt_0adf3d2940014EUTSJsZMZzLsq", "sessionID": "ses_f520d514dffeuvK2rSnqu4hevA", "messageID": "msg_0adf2fe16001uJKXQFdSU2ZAsi" } ] } ] }