{"task": {"agent_timeout": 600, "task": "815", "verifier_timeout": 7200, "instruction": "Please implement a Python 3 solution to the below problem.\nReason through the problem and:\n1. Restate the problem in plain English\n2. Conceptualize a solution first in plain English\n3. Write a pseudocode solution\n4. Save your solution as solution.py\nNo outside libraries are allowed.\n\n[BEGIN PROBLEM]\nEarly in the morning, Farmer John woke up to the sound of splintering wood. It\nwas the cows, and they were breaking out of the barn again!\n\nFarmer John was sick and tired of the cows' morning breakouts, and he decided\nenough was enough: it was time to get tough. He nailed to the barn wall a\ncounter tracking the number of days since the last breakout. So if a breakout\noccurred in the morning, the counter would be $0$ that day; if the most recent\nbreakout was $3$ days ago, the counter would read $3$. Farmer John meticulously\nlogged the counter every day.\n\nThe end of the year has come, and Farmer John is ready to do some accounting.\nThe cows will pay, he says! But something about his log doesn't look quite\nright...  \n\nFarmer John wants to find out how many breakouts have occurred since he started\nhis log. However, he suspects that the cows have tampered with his log, and all\nhe knows for sure is that he started his log on the day of a breakout. Please\nhelp him determine, for each number of breakouts that might have occurred since\nhe started the log, the minimum number of log entries that must have been\ntampered with.\n\nINPUT FORMAT:\nThe first line contains a single integer $N$ ($1 \\leq N \\leq 100$), denoting the\nnumber of days since Farmer John started logging the cow breakout counter.\n\nThe second line contains $N$ space-separated integers. The $i$th integer is a\nnon-negative integer $a_i$ (at most $100$), indicating that on day $i$ the\ncounter was at $a_i$, unless the cows tampered with that day's log entry.\n\nOUTPUT FORMAT:\nThe output should consist of $N$ integers, one per line. The $i$th\ninteger should be the minimum over all possible breakout sequences with $i$\nbreakouts, of the number of log entries that are inconsistent with that\nsequence.\n\nSAMPLE INPUT:\n6\n1 1 2 0 0 1\nSAMPLE OUTPUT: \n4\n2\n1\n2\n3\n4\n\nIf there was only 1 breakout, then the correct log would look like 0 1 2 3 4 5,\nwhich is 4 entries different from the given log.\n\nIf there were 2 breakouts, then the correct log might look like 0 1 2 3 0 1,\nwhich is 2 entries different from the given log. In this case, the breakouts\noccurred on the first and fifth days.\n\nIf there were 3 breakouts, then the correct log might look like 0 1 2 0 0 1,\nwhich is just 1 entry different from the given log. In this case, the breakouts\noccurred on the first, fourth, and fifth days.\n\nAnd so on.\n\n\nProblem credits: Brian Dean and Dhruv Rohatgi\n\n[END PROBLEM]\n", "memory": "2048m", "runnable": false, "difficulty": "medium", "language": "", "cpus": 1, "instruction_truncated": false, "category": "python_programming", "compose": false, "has_solution": true, "oracle": null, "docker_image": "", "taskset": "usaco", "tags": ["python", "programming", "usaco"]}, "runs": []}