A14215 | AND Sequences
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题目描述
A sequence of $n$ non-negative integers ( $n \ge 2$ ) $a_1, a_2, \dots, a_n$ is called good if for all $i$ from $1$ to $n-1$ the following condition holds true: $$$$a_1 \: \& \: a_2 \: \& \: \dots \: \& \: a_i = a_{i+1} \: \& \: a_{i+2} \: \& \: \dots \: \& \: a_n, $$ where $\\&$ denotes the <a href="https://en.wikipedia.org/wiki/Bitwise_operation#AND">bitwise AND operation</a>.</p><p>You are given an array $a$ of size $n$ ( $n \\geq 2$ ). Find the number of permutations $p$ of numbers ranging from $1$ to $n$ , for which the sequence $a\_{p\_1}$ , $a\_{p\_2}$ , ... , $a\_{p\_n}$ is good. Since this number can be large, output it modulo $10^9+7$$$.
输入格式
The first line contains a single integer $t$ ( $1 \leq t \leq 10^4$ ), denoting the number of test cases.
The first line of each test case contains a single integer $n$ ( $2 \le n \le 2 \cdot 10^5$ ) — the size of the array.
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $0 \le a_i \le 10^9$ ) — the elements of the array.
It is guaranteed that the sum of $n$ over all test cases doesn't exceed $2 \cdot 10^5$ .
The first line of each test case contains a single integer $n$ ( $2 \le n \le 2 \cdot 10^5$ ) — the size of the array.
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $0 \le a_i \le 10^9$ ) — the elements of the array.
It is guaranteed that the sum of $n$ over all test cases doesn't exceed $2 \cdot 10^5$ .
输出格式
Output $t$ lines, where the $i$ -th line contains the number of good permutations in the $i$ -th test case modulo $10^9 + 7$ .
输入输出样例
输入 #1
4 3 1 1 1 5 1 2 3 4 5 5 0 2 0 3 0 4 1 3 5 1
输出 #1
6 0 36 4
In the first test case, since all the numbers are equal, whatever permutation we take, the sequence is good. There are a total of $6$ permutations possible with numbers from $1$ to $3$ : $[1,2,3]$ , $[1,3,2]$ , $[2,1,3]$ , $[2,3,1]$ , $[3,1,2]$ , $[3,2,1]$ .
In the second test case, it can be proved that no permutation exists for which the sequence is good.
In the third test case, there are a total of $36$ permutations for which the sequence is good. One of them is the permutation $[1,5,4,2,3]$ which results in the sequence $s=[0,0,3,2,0]$ . This is a good sequence because
- $ s_1 = s_2 \: \& \: s_3 \: \& \: s_4 \: \& \: s_5 = 0$ ,
- $ s_1 \: \& \: s_2 = s_3 \: \& \: s_4 \: \& \: s_5 = 0$ ,
- $ s_1 \: \& \: s_2 \: \& \: s_3 = s_4 \: \& \: s_5 = 0$ ,
- $ s_1 \: \& \: s_2 \: \& \: s_3 \: \& \: s_4 = s_5 = 0$ .
In the second test case, it can be proved that no permutation exists for which the sequence is good.
In the third test case, there are a total of $36$ permutations for which the sequence is good. One of them is the permutation $[1,5,4,2,3]$ which results in the sequence $s=[0,0,3,2,0]$ . This is a good sequence because
- $ s_1 = s_2 \: \& \: s_3 \: \& \: s_4 \: \& \: s_5 = 0$ ,
- $ s_1 \: \& \: s_2 = s_3 \: \& \: s_4 \: \& \: s_5 = 0$ ,
- $ s_1 \: \& \: s_2 \: \& \: s_3 = s_4 \: \& \: s_5 = 0$ ,
- $ s_1 \: \& \: s_2 \: \& \: s_3 \: \& \: s_4 = s_5 = 0$ .
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评测结果：Accepted