{"trustable":true,"sections":[{"title":"","value":{"format":"HTML","content":"\u003cpre\u003e\u003ch2\u003eDescription\u003c/h2\u003e\n\nKeeping track of all the cows can be a tricky task so Farmer John has installed a system \nto automate it. He has installed on each cow an electronic ID tag that the system will \nread as the cows pass by a scanner. Each ID tag\u0027s contents are currently a single string \nwith length M (1 ≤ M ≤ 2,000) characters drawn from an alphabet of N (1 ≤ N ≤ 26) \ndifferent symbols (namely, the lower-case roman alphabet).\nCows, being the mischievous creatures they are, sometimes try to spoof the system by walking \nbackwards. While a cow whose ID is \"abcba\" would read the same no matter which direction the \nshe walks, a cow with the ID \"abcb\" can potentially register as two different IDs (\"abcb\" \nand \"bcba\").\n\nFJ would like to change the cows\u0027s ID tags so they read the same no matter which direction \nthe cow walks by. For example, \"abcb\" can be changed by adding \"a\" at the end to form \"abcba\" \nso that the ID is palindromic (reads the same forwards and backwards). Some other ways to change \nthe ID to be palindromic are include adding the three letters \"bcb\" to the begining to yield the \nID \"bcbabcb\" or removing the letter \"a\" to yield the ID \"bcb\". One can add or remove characters \nat any location in the string yielding a string longer or shorter than the original string.\n\nUnfortunately as the ID tags are electronic, each character insertion or deletion has a cost \n(0 ≤ cost ≤ 10,000) which varies depending on exactly which character value to be added or \ndeleted. Given the content of a cow\u0027s ID tag and the cost of inserting or deleting each of the \nalphabet\u0027s characters, find the minimum cost to change the ID tag so it satisfies FJ\u0027s requirements. \nAn empty ID tag is considered to satisfy the requirements of reading the same forward and backward. \nOnly letters with associated costs can be added to a string.\n\n\u003ch2\u003eInput\u003c/h2\u003e\n\n* Line 1: Two space-separated integers: N and M \n* Line 2: This line contains exactly M characters which constitute the initial ID string\n* Lines 3..N + 2: Each line contains three space-separated entities: a character of the input alphabet \nand two integers which are respectively the cost of adding and deleting that character.\n\n\n\u003ch2\u003eOutput\u003c/h2\u003e\n\n* Line 1: A single line with a single integer that is the minimum cost to change the given name tag.\n\n\u003ch2\u003eSample Input\u003c/h2\u003e\n\n3 4\nabcb\na 1000 1100\nb 350 700\nc 200 800\n\n\u003ch2\u003eSample Output\u003c/h2\u003e\n\n900\n\n\u003ch2\u003eHint\u003c/h2\u003e\n\nThe nametag is \"abcb\" with these per-operation costs:\n\n Insert Delete\na 1000 1100\nb 350 700\nc 200 800\n\n\nIf we insert an \"a\" on the end to get \"abcba\", the cost would be 1000. If we delete the \"a\" on the \nbeginning to get \"bcb\", the cost would be 1100. If we insert \"bcb\" at the begining of the string, \nthe cost would be 350+200+350\u003d900, which is the minimum. \n\n\u003ch2\u003eSource\u003c/h2\u003e\n\nUSACO Open 2007 Gold\n\u003c/pre\u003e"}}]}