{"trustable":true,"prependHtml":"\u003cscript\u003e window.katexOptions \u003d { disable: true }; \u003c/script\u003e\n\u003cscript type\u003d\"text/x-mathjax-config\"\u003e\n MathJax.Hub.Config({\n tex2jax: {\n inlineMath: [[\u0027$$$\u0027,\u0027$$$\u0027], [\u0027$\u0027,\u0027$\u0027]],\n displayMath: [[\u0027$$$$$$\u0027,\u0027$$$$$$\u0027], [\u0027$$\u0027,\u0027$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS-MML_HTMLorMML\" type\u003d\"text/javascript\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"panel_content\"\u003ePeter has an $n \\times m$ matrix $M$. Let $S(a,b)$ be the sum of the weight all $a \\times b$ submatrices of $M$. The weight of matrix is the sum of the value of all the saddle points in the matrix. A saddle point of a matrix is an element which is both the only largest element in its column and the only smallest element in its row. Help Peter find out all the value of $S(a,b)$.\u003cbr\u003e\u003cbr\u003eNote: the definition of saddle point in this problem may be different with the definition you knew before.\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"There are multiple test cases. The first line of input contains an integer $T$, indicating the number of test cases. For each test case:\u003cbr\u003e\u003cbr\u003eThe first contains two integers $n$ and $m$ $(1 \\le n, m \\le 1000)$ -- the dimensions of the matrix.\u003cbr\u003e\u003cbr\u003eThe next $n$ lines each contain $m$ non-negative integers separated by spaces describing rows of matrix $M$ (each element of $M$ is no greater than $10^6$)."}},{"title":"Output","value":{"format":"HTML","content":"For each test case, output an integer $W \u003d (\\displaystyle\\sum_{a\u003d1}^{n}\\sum_{b\u003d1}^{m}{a \\cdot b \\cdot S(a,b)}) \\text{ mod } 2^{32}$."}},{"title":"Sample","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\r\n2 2\r\n1 1\r\n1 1\r\n3 3\r\n1 2 3\r\n4 5 6\r\n7 8 9\r\n3 3\r\n1 2 1\r\n2 3 1\r\n4 5 2\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e4\r\n600\r\n215\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}