10885: ABC358 - E - Alphabet Tiles
[Creator : ]
Description
Problem Statement
AtCoder Land sells tiles with English letters written on them. Takahashi is thinking of making a nameplate by arranging these tiles in a row.
Find the number, modulo $998244353$, of strings consisting of uppercase English letters with a length between $1$ and $K$, inclusive, that satisfy the following conditions:
- For every integer $i$ satisfying $1 \leq i \leq 26$, the following holds:
- Let $a_i$ be the $i$-th uppercase English letter in lexicographical order. For example, $a_1 = $
A, $a_5 = $E, $a_{26} = $Z. - The number of occurrences of $a_i$ in the string is between $0$ and $C_i$, inclusive.
- Let $a_i$ be the $i$-th uppercase English letter in lexicographical order. For example, $a_1 = $
Input
The input is given from Standard Input in the following format:
```
$K$
$C_1$ $C_2$ $\ldots$ $C_{26}$
```
```
$K$
$C_1$ $C_2$ $\ldots$ $C_{26}$
```
Output
Print the answer.
Constraints
- $1 \leq K \leq 1000$
- $0 \leq C_i \leq 1000$
- All input values are integers.
- $0 \leq C_i \leq 1000$
- All input values are integers.
Sample 1 Input
2
2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Sample 1 Output
10
The $10$ strings that satisfy the conditions are A, B, C, AA, AB, AC, BA, BC, CA, CB.
Sample 2 Input
358
1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Sample 2 Output
64
Sample 3 Input
1000
1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000
Sample 3 Output
270274035