AtCoder Regular Contest 084
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Problem Statement
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There are $N$ non-negative integers written on a blackboard. The $i$-th integer is $A_i$.
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Takahashi can perform the following two kinds of operations any number of times in any order:
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- Select one integer written on the board (let this integer be
$X$). Write$2X$on the board, without erasing the selected integer. - Select two integers, possibly the same, written on the board (let these integers be
$X$and$Y$). Write$X$XOR$Y$(XOR stands for bitwise xor) on the blackboard, without erasing the selected integers.
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How many different integers not exceeding $X$ can be written on the blackboard? We will also count the integers that are initially written on the board. Since the answer can be extremely large, find the count modulo $998244353$.
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Constraints
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$1 \leq N \leq 6$$1 \leq X < 2^{4000}$$1 \leq A_i < 2^{4000}(1\leq i\leq N)$- All input values are integers.
$X$and$A_i(1\leq i\leq N)$are given in binary notation, with the most significant digit in each of them being$1$.
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Input
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Input is given from Standard Input in the following format:
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N X
A_1
:
A_N翻译中…
Output
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Print the number of different integers not exceeding $X$ that can be written on the blackboard.
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样例
Input #1
3 111
1111
10111
10010
Output #1
4
Initially, $15$, $23$ and $18$ are written on the blackboard. Among the integers not exceeding $7$, four integers, $0$, $3$, $5$ and $6$, can be written. For example, $6$ can be written as follows:
- Double $15$ to write $30$.
- Take XOR of $30$ and $18$ to write $12$.
- Double $12$ to write $24$.
- Take XOR of $30$ and $24$ to write $6$.
Input #2
4 100100
1011
1110
110101
1010110
Output #2
37
Input #3
4 111001100101001
10111110
1001000110
100000101
11110000011
Output #3
1843
Input #4
1 111111111111111111111111111111111111111111111111111111111111111
1
Output #4
466025955
Be sure to find the count modulo $998244353$.
题目信息
题面与样例版权归 AtCoder 及出题人所有；中文翻译由 AI 生成（CI 管线），如有出入请以原文为准。