{"problem":{"name":"ABC Tournament","description":{"content":"$2^N$ players, labeled $1$ through $2^N$, will compete against each other in a single-elimination programming tournament.   The rating of Player $i$ is $A_i$. Any two players have different ratings, a","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc188_c"},"statements":[{"statement_type":"Markdown","content":"$2^N$ players, labeled $1$ through $2^N$, will compete against each other in a single-elimination programming tournament.  \nThe rating of Player $i$ is $A_i$. Any two players have different ratings, and a match between two players always results in the victory of the player with the higher rating.\nThe tournament looks like a perfect binary tree.  \nFormally, the tournament will proceed as follows:\n\n*   For each integer $i = 1, 2, 3, \\dots, N$ in this order, the following happens.\n    *   For each integer $j (1 \\le j \\le 2^{N - i})$, among the players who have never lost, the player with the $(2j - 1)$\\-th smallest label and the player with the $2j$\\-th smallest label play a match against each other.\n\nFind the label of the player who will take **second place**, that is, lose in the final match.\n\n## Constraints\n\n*   $1 \\le N \\le 16$\n*   $1 \\le A_i \\le 10^9$\n*   $A_i$ are pairwise different.\n*   All values in input are integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$\n$A_1$ $A_2$ $A_3$ $\\dots$ $A_{2^N}$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc188_c","tags":[],"sample_group":[["2\n1 4 2 5","2\n\nFirst, there will be two matches between Players $1$ and $2$ and between Players $3$ and $4$. According to the ratings, Players $2$ and $4$ will win.  \nThen, there will be a match between Players $2$ and $4$, and the tournament will end with Player $4$ becoming champion.  \nThe player who will lose in the final match is Player $2$, so we should print $2$."],["2\n3 1 5 4","1\n\nFirst, there will be two matches between Players $1$ and $2$ and between Players $3$ and $4$. According to the ratings, Players $1$ and $3$ will win.  \nThen, there will be a match between Players $1$ and $3$, and the tournament will end with Player $3$ becoming champion.  \nThe player who will lose in the final match is Player $1$, so we should print $1$."],["4\n6 13 12 5 3 7 10 11 16 9 8 15 2 1 14 4","2"]],"created_at":"2026-03-03 11:01:14"}}