{"trustable":true,"prependHtml":"\u003cstyle type\u003d\"text/css\"\u003e\n section pre {\n display: block;\n padding: 9.5px;\n margin: 0 0 10px;\n font-size: 13px;\n line-height: 1.42857143;\n word-break: break-all;\n word-wrap: break-word;\n color: #333;\n background: rgba(255, 255, 255, 0.5);\n border: 1px solid #ccc;\n border-radius: 6px;\n }\n\u003c/style\u003e\n\u003cscript\u003e\n window.katexOptions \u003d {\n delimiters: [\n {left: \u0027\\\\(\u0027, right: \u0027\\\\)\u0027, display: false},\n {left: \u0027\\\\[\u0027, right: \u0027\\\\]\u0027, display: true}\n ]\n };\n\u003c/script\u003e\n","sections":[{"title":"Problem Statement","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cp\u003eJoisino the magical girl has decided to turn every single digit that exists on this world into \u003cvar\u003e\\(1\\)\u003c/var\u003e.\u003c/p\u003e\r\n\u003cp\u003eRewriting a digit \u003cvar\u003e\\(i\\)\u003c/var\u003e with \u003cvar\u003e\\(j\\)\u003c/var\u003e \u003cvar\u003e\\((0≤i,j≤9)\\)\u003c/var\u003e costs \u003cvar\u003e\\(c_{i,j}\\)\u003c/var\u003e MP (Magic Points).\u003c/p\u003e\r\n\u003cp\u003eShe is now standing before a wall. The wall is divided into \u003cvar\u003e\\(HW\\)\u003c/var\u003e squares in \u003cvar\u003e\\(H\\)\u003c/var\u003e rows and \u003cvar\u003e\\(W\\)\u003c/var\u003e columns, and at least one square contains a digit between \u003cvar\u003e\\(0\\)\u003c/var\u003e and \u003cvar\u003e\\(9\\)\u003c/var\u003e (inclusive).\u003c/p\u003e\r\n\u003cp\u003eYou are given \u003cvar\u003e\\(A_{i,j}\\)\u003c/var\u003e that describes the square at the \u003cvar\u003e\\(i\\)\u003c/var\u003e-th row from the top and \u003cvar\u003e\\(j\\)\u003c/var\u003e-th column from the left, as follows:\u003c/p\u003e\r\n\u003cul\u003e\r\n\u003cli\u003eIf \u003cvar\u003e\\(A_{i,j}≠-1\\)\u003c/var\u003e, the square contains a digit \u003cvar\u003e\\(A_{i,j}\\)\u003c/var\u003e.\u003c/li\u003e\r\n\u003cli\u003eIf \u003cvar\u003e\\(A_{i,j}\u003d-1\\)\u003c/var\u003e, the square does not contain a digit.\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003cp\u003eFind the minimum total amount of MP required to turn every digit on this wall into \u003cvar\u003e\\(1\\)\u003c/var\u003e in the end.\u003c/p\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Constraints","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cul\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(1≤H,W≤200\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(1≤c_{i,j}≤10^3\\)\u003c/var\u003e \u003cvar\u003e\\((i≠j)\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(c_{i,j}\u003d0\\)\u003c/var\u003e \u003cvar\u003e\\((i\u003dj)\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(-1≤A_{i,j}≤9\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003eAll input values are integers.\u003c/li\u003e\r\n\u003cli\u003eThere is at least one digit on the wall.\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Input","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cp\u003eInput is given from Standard Input in the following format:\u003c/p\u003e\r\n\u003cpre\u003e\u003cvar\u003e\\(H\\)\u003c/var\u003e \u003cvar\u003e\\(W\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(c_{0,0}\\)\u003c/var\u003e \u003cvar\u003e\\(...\\)\u003c/var\u003e \u003cvar\u003e\\(c_{0,9}\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(:\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(c_{9,0}\\)\u003c/var\u003e \u003cvar\u003e\\(...\\)\u003c/var\u003e \u003cvar\u003e\\(c_{9,9}\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(A_{1,1}\\)\u003c/var\u003e \u003cvar\u003e\\(...\\)\u003c/var\u003e \u003cvar\u003e\\(A_{1,W}\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(:\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(A_{H,1}\\)\u003c/var\u003e \u003cvar\u003e\\(...\\)\u003c/var\u003e \u003cvar\u003e\\(A_{H,W}\\)\u003c/var\u003e\r\n\u003c/pre\u003e\r\n\r\n\u003c/section\u003e\r\n"}},{"title":"Output","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cp\u003ePrint the minimum total amount of MP required to turn every digit on the wall into \u003cvar\u003e\\(1\\)\u003c/var\u003e in the end.\u003c/p\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Sample 1","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e2 4\r\n0 9 9 9 9 9 9 9 9 9\r\n9 0 9 9 9 9 9 9 9 9\r\n9 9 0 9 9 9 9 9 9 9\r\n9 9 9 0 9 9 9 9 9 9\r\n9 9 9 9 0 9 9 9 9 2\r\n9 9 9 9 9 0 9 9 9 9\r\n9 9 9 9 9 9 0 9 9 9\r\n9 9 9 9 9 9 9 0 9 9\r\n9 9 9 9 2 9 9 9 0 9\r\n9 2 9 9 9 9 9 9 9 0\r\n-1 -1 -1 -1\r\n8 1 1 8\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e12\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003cp\u003eTo turn a single \u003cvar\u003e\\(8\\)\u003c/var\u003e into \u003cvar\u003e\\(1\\)\u003c/var\u003e, it is optimal to first turn \u003cvar\u003e\\(8\\)\u003c/var\u003e into \u003cvar\u003e\\(4\\)\u003c/var\u003e, then turn \u003cvar\u003e\\(4\\)\u003c/var\u003e into \u003cvar\u003e\\(9\\)\u003c/var\u003e, and finally turn \u003cvar\u003e\\(9\\)\u003c/var\u003e into \u003cvar\u003e\\(1\\)\u003c/var\u003e, costing \u003cvar\u003e\\(6\\)\u003c/var\u003e MP.\u003c/p\u003e\r\n\u003cp\u003eThe wall contains two \u003cvar\u003e\\(8\\)\u003c/var\u003es, so the minimum total MP required is \u003cvar\u003e\\(6×2\u003d12\\)\u003c/var\u003e.\u003c/p\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Sample 2","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e5 5\r\n0 999 999 999 999 999 999 999 999 999\r\n999 0 999 999 999 999 999 999 999 999\r\n999 999 0 999 999 999 999 999 999 999\r\n999 999 999 0 999 999 999 999 999 999\r\n999 999 999 999 0 999 999 999 999 999\r\n999 999 999 999 999 0 999 999 999 999\r\n999 999 999 999 999 999 0 999 999 999\r\n999 999 999 999 999 999 999 0 999 999\r\n999 999 999 999 999 999 999 999 0 999\r\n999 999 999 999 999 999 999 999 999 0\r\n1 1 1 1 1\r\n1 1 1 1 1\r\n1 1 1 1 1\r\n1 1 1 1 1\r\n1 1 1 1 1\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e0\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003cp\u003eNote that she may not need to change any digit.\u003c/p\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Sample 3","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e3 5\r\n0 4 3 6 2 7 2 5 3 3\r\n4 0 5 3 7 5 3 7 2 7\r\n5 7 0 7 2 9 3 2 9 1\r\n3 6 2 0 2 4 6 4 2 3\r\n3 5 7 4 0 6 9 7 6 7\r\n9 8 5 2 2 0 4 7 6 5\r\n5 4 6 3 2 3 0 5 4 3\r\n3 6 2 3 4 2 4 0 8 9\r\n4 6 5 4 3 5 3 2 0 8\r\n2 1 3 4 5 7 8 6 4 0\r\n3 5 2 6 1\r\n2 5 3 2 1\r\n6 9 2 5 6\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e47\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\r\n\u003csection\u003e\r\n\r\n\r\n\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\u003c/section\u003e\r\n"}}]}