{"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\u003eWe have \u003cvar\u003e\\(N\\)\u003c/var\u003e oranges, numbered \u003cvar\u003e\\(1\\)\u003c/var\u003e through \u003cvar\u003e\\(N\\)\u003c/var\u003e.\r\nThe weight of Orange \u003cvar\u003e\\(i\\)\u003c/var\u003e is \u003cvar\u003e\\(W_i\\)\u003c/var\u003e.\r\nTakahashi and Aoki will share these oranges as follows.\u003c/p\u003e\r\n\u003cul\u003e\r\n\u003cli\u003e\r\n\u003cp\u003eChoose a permutation \u003cvar\u003e\\((p_1, p_2, \\cdots, p_N)\\)\u003c/var\u003e of \u003cvar\u003e\\((1,2,\\cdots,N)\\)\u003c/var\u003e.\u003c/p\u003e\r\n\u003c/li\u003e\r\n\u003cli\u003e\r\n\u003cp\u003eFor each \u003cvar\u003e\\(i \u003d 1, 2, \\cdots, N\\)\u003c/var\u003e in this order, do the following.\u003c/p\u003e\r\n\u003cul\u003e\r\n\u003cli\u003eIf the total weight of the oranges Takahashi has taken is not greater than that of the oranges Aoki has taken, Takahashi takes Orange \u003cvar\u003e\\(p_i\\)\u003c/var\u003e.\r\nOtherwise, Aoki takes Orange \u003cvar\u003e\\(p_i\\)\u003c/var\u003e.\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003cp\u003eFind the number of permutations \u003cvar\u003e\\(p\\)\u003c/var\u003e modulo \u003cvar\u003e\\(998244353\\)\u003c/var\u003e such that the total weight of the oranges Takahashi will take is equal to that of the oranges Aoki will take.\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\\(2 \\leq N \\leq 100\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(1 \\leq W_i \\leq 100\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003eAll values in input are integers.\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\\(N\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(W_1\\)\u003c/var\u003e \u003cvar\u003e\\(W_2\\)\u003c/var\u003e \u003cvar\u003e\\(\\cdots\\)\u003c/var\u003e \u003cvar\u003e\\(W_N\\)\u003c/var\u003e\r\n\u003c/pre\u003e\r\n\u003c/section\u003e\r\n"}},{"title":"Output","value":{"format":"HTML","content":"\r\n\u003csection\u003e\r\n\u003cp\u003ePrint the answer.\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\u003e3\r\n1 1 2\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e4\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\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\r\n\u003cp\u003eThere are four permutations \u003cvar\u003e\\(p\\)\u003c/var\u003e satisfying the condition: \u003cvar\u003e\\((1,3,2),(2,3,1),(3,1,2),(3,2,1)\\)\u003c/var\u003e.\r\nIf \u003cvar\u003e\\(p\u003d(3,2,1)\\)\u003c/var\u003e, for example, the following will happen.\u003c/p\u003e\r\n\u003cul\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(i\u003d1\\)\u003c/var\u003e: the total weights of the oranges Takahashi and Aoki have taken are \u003cvar\u003e\\(0\\)\u003c/var\u003e and \u003cvar\u003e\\(0\\)\u003c/var\u003e, respectively. Takahashi takes Orange \u003cvar\u003e\\(p_i\u003d3\\)\u003c/var\u003e.\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(i\u003d2\\)\u003c/var\u003e: the total weights of the oranges Takahashi and Aoki have taken are \u003cvar\u003e\\(2\\)\u003c/var\u003e and \u003cvar\u003e\\(0\\)\u003c/var\u003e, respectively. Aoki takes Orange \u003cvar\u003e\\(p_i\u003d2\\)\u003c/var\u003e.\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(i\u003d3\\)\u003c/var\u003e: the total weights of the oranges Takahashi and Aoki have taken are \u003cvar\u003e\\(2\\)\u003c/var\u003e and \u003cvar\u003e\\(1\\)\u003c/var\u003e, respectively. Aoki takes Orange \u003cvar\u003e\\(p_i\u003d1\\)\u003c/var\u003e.\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003cp\u003eThus, the permutation \u003cvar\u003e\\(p\u003d(3,2,1)\\)\u003c/var\u003e counts.\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\u003e4\r\n1 2 3 8\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\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\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\u003e20\r\n2 8 4 7 5 3 1 2 4 1 2 5 4 3 3 8 1 7 8 2\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e373835282\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\u003c/section\u003e\r\n\r\n\u003csection\u003e\r\n\u003c/section\u003e\r\n"}}]}