AtCoder Regular Contest 162
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Problem Statement
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You are given a sequence of length $N$ consisting of integers from $1$ to $N$, $A=(A_1,A_2,\ldots,A_N)$.
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Find the number, modulo $998244353$, of sequences of length $N$ consisting of integers from $1$ to $N$, $B=(B_1,B_2,\ldots,B_N)$, that satisfy the following conditions for all $i=1,2,\ldots,N$.
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- The number of occurrences of
$i$in$B$is at most$A_i$. - The number of occurrences of
$B_i$in$B$is at most$A_i$.
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Constraints
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$1 \leq N \leq 500$$1 \leq A_i \leq N$- All input values are integers.
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Input
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The input is given from Standard Input in the following format:
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N
A_1 A_2 \ldots A_N翻译中…
Output
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Print the answer.
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样例
Input #1
3
1 2 3
Output #1
10
The following $10$ sequences satisfy the conditions:
- $(1,2,2)$
- $(1,2,3)$
- $(1,3,2)$
- $(1,3,3)$
- $(2,1,3)$
- $(2,3,1)$
- $(2,3,3)$
- $(3,1,2)$
- $(3,2,1)$
- $(3,2,2)$
Input #2
4
4 4 4 4
Output #2
256
All sequences of length $4$ consisting of integers from $1$ to $4$ satisfy the conditions, and there are $4^4=256$ such sequences.
Input #3
5
1 1 1 1 1
Output #3
120
All permutations of $(1,2,3,4,5)$ satisfy the conditions, and there are $5!=120$ such sequences.
Input #4
14
6 5 14 3 6 7 3 11 11 2 3 7 8 10
Output #4
628377683
Be sure to print the number 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。