{"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 points numbered \u003cvar\u003e\\(1\\)\u003c/var\u003e to \u003cvar\u003e\\(N\\)\u003c/var\u003e arranged in a line in this order.\u003c/p\u003e\r\n\u003cp\u003eTakahashi decides to make an undirected graph, using these points as the vertices.\r\nIn the beginning, the graph has no edge. Takahashi will do \u003cvar\u003e\\(M\\)\u003c/var\u003e operations to add edges in this graph.\r\nThe \u003cvar\u003e\\(i\\)\u003c/var\u003e-th operation is as follows:\u003c/p\u003e\r\n\u003cul\u003e\r\n\u003cli\u003eThe operation uses integers \u003cvar\u003e\\(L_i\\)\u003c/var\u003e and \u003cvar\u003e\\(R_i\\)\u003c/var\u003e between \u003cvar\u003e\\(1\\)\u003c/var\u003e and \u003cvar\u003e\\(N\\)\u003c/var\u003e (inclusive), and a positive integer \u003cvar\u003e\\(C_i\\)\u003c/var\u003e. For every pair of integers \u003cvar\u003e\\((s, t)\\)\u003c/var\u003e such that \u003cvar\u003e\\(L_i \\leq s \u0026lt; t \\leq R_i\\)\u003c/var\u003e, add an edge of length \u003cvar\u003e\\(C_i\\)\u003c/var\u003e between Vertex \u003cvar\u003e\\(s\\)\u003c/var\u003e and Vertex \u003cvar\u003e\\(t\\)\u003c/var\u003e.\u003c/li\u003e\r\n\u003c/ul\u003e\r\n\u003cp\u003eThe integers \u003cvar\u003e\\(L_1, ..., L_M\\)\u003c/var\u003e, \u003cvar\u003e\\(R_1, ..., R_M\\)\u003c/var\u003e, \u003cvar\u003e\\(C_1, ..., C_M\\)\u003c/var\u003e are all given as input.\u003c/p\u003e\r\n\u003cp\u003eTakahashi wants to solve the shortest path problem in the final graph obtained. Find the length of the shortest path from Vertex \u003cvar\u003e\\(1\\)\u003c/var\u003e to Vertex \u003cvar\u003e\\(N\\)\u003c/var\u003e in the final graph.\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 10^5\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(1 \\leq M \\leq 10^5\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(1 \\leq L_i \u0026lt; R_i \\leq N\\)\u003c/var\u003e\u003c/li\u003e\r\n\u003cli\u003e\u003cvar\u003e\\(1 \\leq C_i \\leq 10^9\\)\u003c/var\u003e\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 \u003cvar\u003e\\(M\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(L_1\\)\u003c/var\u003e \u003cvar\u003e\\(R_1\\)\u003c/var\u003e \u003cvar\u003e\\(C_1\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(:\\)\u003c/var\u003e\r\n\u003cvar\u003e\\(L_M\\)\u003c/var\u003e \u003cvar\u003e\\(R_M\\)\u003c/var\u003e \u003cvar\u003e\\(C_M\\)\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 length of the shortest path from Vertex \u003cvar\u003e\\(1\\)\u003c/var\u003e to Vertex \u003cvar\u003e\\(N\\)\u003c/var\u003e in the final graph.\r\nIf there is no shortest path, print \u003ccode\u003e-1\u003c/code\u003e instead.\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\u003e4 3\r\n1 3 2\r\n2 4 3\r\n1 4 6\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e5\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\u003eWe have an edge of length \u003cvar\u003e\\(2\\)\u003c/var\u003e between Vertex \u003cvar\u003e\\(1\\)\u003c/var\u003e and Vertex \u003cvar\u003e\\(2\\)\u003c/var\u003e, and an edge of length \u003cvar\u003e\\(3\\)\u003c/var\u003e between Vertex \u003cvar\u003e\\(2\\)\u003c/var\u003e and Vertex \u003cvar\u003e\\(4\\)\u003c/var\u003e, so there is a path of length \u003cvar\u003e\\(5\\)\u003c/var\u003e between Vertex \u003cvar\u003e\\(1\\)\u003c/var\u003e and Vertex \u003cvar\u003e\\(4\\)\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\u003e4 2\r\n1 2 1\r\n3 4 2\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e-1\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\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\u003e10 7\r\n1 5 18\r\n3 4 8\r\n1 3 5\r\n4 7 10\r\n5 9 8\r\n6 10 5\r\n8 10 3\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e28\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"}}]}