{"task": {"agent_timeout": 600, "task": "809", "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 lo and behold, some entries of his log are\nmissing!  \n\nFarmer John is confident that the he started his log on the day of a breakout. \nPlease help him determine, out of all sequences of events consistent with the\nlog entries that remain, the minimum and maximum number of breakouts that may\nhave take place over the course of the logged time. \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\neither $-1$, indicating that the log entry for day $i$ is missing, or a\nnon-negative integer $a_i$ (at most $100$), indicating that on day $i$ the counter\nwas at\n$a_i$.\n\nOUTPUT FORMAT:\nIf there is no sequence of events consistent with Farmer John's partial log and\nhis knowledge that the cows definitely broke out of the barn on the morning of\nday $1$, output a single integer $-1$.  Otherwise, output two space-separated\nintegers $m$ followed by $M$, where $m$ is the minimum number of breakouts of\nany consistent sequence of events, and $M$ is the maximum.\n\nSAMPLE INPUT:\n4\n-1 -1 -1 1\nSAMPLE OUTPUT: \n2 3\n\nIn this example, we can deduce that a breakout had to occur on day 3.  Knowing\nthat  a breakout also occurred on day 1, the only remaining bit of uncertainty\nis whether a breakout occurred on day 2.  Hence, there were between 2 and 3\nbreakouts in total.\n\nProblem credits: 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": []}