{"problem":{"name":"CatCoder Double Contest","description":{"content":"> The problem setting of this problem is partially shared with Problem F. In the year $2222$, CatCoder will hold the CatCoder Double Contest (abbreviated as C2C). There are $N$ writers who have probl","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc201_a"},"statements":[{"statement_type":"Markdown","content":"> The problem setting of this problem is partially shared with Problem F.\n\nIn the year $2222$, CatCoder will hold the CatCoder Double Contest (abbreviated as C2C).\nThere are $N$ writers who have problem proposals. Each writer's problem proposals are classified into $3$ types by difficulty: Hard, Medium, Easy, and the $i$\\-th writer has $A_i$, $B_i$, $C_i$ problem proposals of Hard, Medium, Easy, respectively.\nEach C2C simultaneously holds $2$ divisions, Div.1 and Div.2. The problem proposals required for each division are as follows:\n\n*   Div.1: One Hard and one Medium problem proposal from the same writer\n*   Div.2: One Medium and one Easy problem proposal from the same writer\n\nNote that **the writers for Div.1 and Div.2 do not necessarily have to be the same**. Also, each problem proposal can be used in at most one division of one C2C.\nFind the maximum number of times C2C can be held.\n$T$ test cases are given, so find the answer for each.\n\n## Constraints\n\n*   $1 \\le T \\le 10^5$\n*   $1 \\le N \\le 2 \\times 10^5$\n*   $1 \\le A_i,B_i,C_i \\le 10^9$\n*   The sum of $N$ over all test cases is at most $2 \\times 10^5$.\n*   All input values are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$T$\n$\\text{case}_1$\n$\\text{case}_2$\n$\\vdots$\n$\\text{case}_T$\n\nEach test case is given in the following format:\n\n$N$\n$A_1$ $B_1$ $C_1$\n$A_2$ $B_2$ $C_2$\n$\\vdots$\n$A_N$ $B_N$ $C_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc201_a","tags":[],"sample_group":[["5\n2\n3 1 4\n1 5 3\n1\n1 1 1\n3\n5 7 5\n1 11 99\n3 1 2\n5\n1000000000 1000000000 1000000000\n1000000000 1000000000 1000000000\n1000000000 1000000000 1000000000\n1000000000 1000000000 1000000000\n1000000000 1000000000 1000000000\n6\n835549144 866512240 105679868\n473233032 625162103 823002638\n125467290 37501686 380787083\n8043910 721085797 254272563\n97327826 744196952 18713225\n978152989 90127986 33086297","2\n0\n7\n2500000000\n998830769\n\nFor the first test case, C2C can be held $2$ times by using problem proposals as follows:\n\nDiv.1\n\nDiv.2\n\n$1$st time\n\nHard, Medium from the $1$st writer\n\nMedium, Easy from the $2$nd writer\n\n$2$nd time\n\nHard, Medium from the $2$nd writer\n\nMedium, Easy from the $2$nd writer"]],"created_at":"2026-03-03 11:01:14"}}