{"problem":{"name":">=<","description":{"content":"A _fantastic IS_ is an integer sequence of length $N$ whose every element is between $1$ and $M$ (inclusive) that satisfies the following condition. *   For every integer $i$ such that $1 \\le i \\le K","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":4000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc146_d"},"statements":[{"statement_type":"Markdown","content":"A _fantastic IS_ is an integer sequence of length $N$ whose every element is between $1$ and $M$ (inclusive) that satisfies the following condition.\n\n*   For every integer $i$ such that $1 \\le i \\le K$, one of the following holds.\n    *   $A_{P_i} < X_i$ and $A_{Q_i} < Y_i$;\n    *   $A_{P_i} = X_i$ and $A_{Q_i} = Y_i$;\n    *   $A_{P_i} > X_i$ and $A_{Q_i} > Y_i$.\n\nDetermine whether a fantastic IS exists. If it does, find the minimum possible sum of the elements in a fantastic IS.\n\n## Constraints\n\n*   $1 \\le N,M,K \\le 2 \\times 10^5$\n*   $1 \\le P_i,Q_i \\le N$\n*   $1 \\le X_i,Y_i \\le M$\n*   $P_i \\neq Q_i$\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $M$ $K$\n$P_1$ $X_1$ $Q_1$ $Y_1$\n$P_2$ $X_2$ $Q_2$ $Y_2$\n$\\vdots$\n$P_K$ $X_K$ $Q_K$ $Y_K$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc146_d","tags":[],"sample_group":[["3 4 3\n3 1 1 2\n1 1 2 2\n3 4 1 4","6\n\n$A=(2,3,1)$ fully satisfies the condition and thus is a fantastic IS, whose sum of the elements is $6$.\nThere is no fantastic IS whose sum of the elements is less than $6$, so the answer is $6$."],["2 2 2\n1 1 2 2\n2 1 1 2","\\-1\n\nThere is no fantastic IS, so $-1$ should be printed."],["5 10 10\n4 1 2 7\n5 1 3 2\n2 9 4 4\n5 4 2 9\n2 9 1 9\n4 8 3 10\n5 7 1 5\n3 5 1 2\n3 8 2 10\n2 9 4 8","12"]],"created_at":"2026-03-03 11:01:14"}}