{"problem":{"name":"Combine to Make Non-decreasing","description":{"content":"You are given an integer sequence of length $N$, $A=(A_1, A_2, \\cdots, A_N)$. Snuke wants to make $A$ a non-decreasing sequence. He can perform the following operation zero or more times. *   Choose ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":3000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"arc207_c"},"statements":[{"statement_type":"Markdown","content":"You are given an integer sequence of length $N$, $A=(A_1, A_2, \\cdots, A_N)$. Snuke wants to make $A$ a non-decreasing sequence.\nHe can perform the following operation zero or more times.\n\n*   Choose two adjacent elements of $A$\n*   Remove these two elements and insert the bitwise $\\mathrm{OR}$ of these two values at the original position\n\nFind the maximum possible value of the length of $A$ when $A$ becomes a non-decreasing sequence.\nWhat is bitwise $\\mathrm{OR}$?The bitwise $\\mathrm{OR}$ of non-negative integers $A$ and $B$, $A\\ \\mathrm{OR}\\ B$, is defined as follows.\n\n*   When $A\\ \\mathrm{OR}\\ B$ is written in binary, the digit in the $2^k$ place ($k \\geq 0$) is $1$ if at least one of the digits in the $2^k$ place of $A$ and $B$ written in binary is $1$, and $0$ otherwise.\n\nFor example, $3\\ \\mathrm{OR}\\ 5 = 7$ (in binary: $011\\ \\mathrm{OR}\\ 101 = 111$).\n\nWhat is a non-decreasing sequence?A sequence $a=(a_1,a_2, \\cdots, a_n)$ is a non-decreasing sequence if and only if $a_1 \\le a_2 \\le \\ldots \\le a_n$ holds.\n\n## Constraints\n\n*   $1 \\le N \\le 2 \\times 10^5$\n*   $1 \\le A_i <2^{30}$\n*   All input values are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$\n$A_1$ $A_2$ $\\ldots$ $A_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"arc207_c","tags":[],"sample_group":[["3\n3 1 2","2\n\n*   If the $1$\\-st and $2$\\-nd elements are chosen in the first operation, $A=(3,2)$ and $A$ is not a non-decreasing sequence.\n*   If the $2$\\-nd and $3$\\-rd elements are chosen in the first operation, $A=(3,3)$ and $A$ is a non-decreasing sequence."],["4\n4 1 2 3","1"],["20\n105327673 847116534 928167271 478716741 244808645 744985167 772409400 950055714 32441819 24475691 74630537 632066724 170250355 937572655 791196964 469960355 264764288 1061830134 183233398 643628719","7"]],"created_at":"2026-03-03 11:01:14"}}