{"problem":{"name":"XOR Partitioning","description":{"content":"The _beauty_ of a sequence $a$ of length $n$ is defined as $a_1 \\oplus \\cdots \\oplus a_n$, where $\\oplus$ denotes the bitwise exclusive or (XOR). You are given a sequence $A$ of length $N$. Snuke will","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"diverta2019_e"},"statements":[{"statement_type":"Markdown","content":"The _beauty_ of a sequence $a$ of length $n$ is defined as $a_1 \\oplus \\cdots \\oplus a_n$, where $\\oplus$ denotes the bitwise exclusive or (XOR).\nYou are given a sequence $A$ of length $N$. Snuke will insert zero or more partitions in $A$ to divide it into some number of non-empty contiguous subsequences.\nThere are $2^{N-1}$ possible ways to insert partitions. How many of them divide $A$ into sequences whose beauties are all equal? Find this count modulo $10^{9}+7$.\n\n## Constraints\n\n*   All values in input are integers.\n*   $1 \\leq N \\leq 5 \\times 10^5$\n*   $0 \\leq A_i < 2^{20}$\n\n## Input\n\nInput 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":"diverta2019_e","tags":[],"sample_group":[["3\n1 2 3","3\n\nFour ways of dividing $A$ shown below satisfy the condition. The condition is not satisfied only if $A$ is divided into $(1),(2),(3)$.\n\n*   $(1,2,3)$\n*   $(1),(2,3)$\n*   $(1,2),(3)$"],["3\n1 2 2","1"],["32\n0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0","147483634\n\nFind the count modulo $10^{9}+7$."],["24\n1 2 5 3 3 6 1 1 8 8 0 3 3 4 6 6 4 0 7 2 5 4 6 2","292"]],"created_at":"2026-03-03 11:01:14"}}