Score : $475$ points

问题陈述

AtCoder Land出售写有英文字母的瓷砖。高桥正在考虑通过排列这些瓷砖来制作一个名牌。

找出满足以下条件的由大写英文字母组成的字符串的数量，长度在$1$到$K$之间（包括两端），对$998244353$取模：

• 对于每个满足$1 \leq i \leq 26$的整数$i$，以下条件成立：
  • 让$a_i$是按字典顺序排列的第$i$个大写英文字母。例如，$a_1 =$ A，$a_5 =$ E，$a_{26} =$ Z。
  • 字符串中$a_i$的出现次数在$0$到$C_i$之间（包括两端）。

以上为大语言模型 kimi 翻译，仅供参考。

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.

Constraints

• $1 \leq K \leq 1000$
• $0 \leq C_i \leq 1000$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

$K$

$C_1$ $C_2$ $\ldots$ $C_{26}$

Output

Print the answer.

Sample Input 1

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 Output 1

10

The $10$ strings that satisfy the conditions are A, B, C, AA, AB, AC, BA, BC, CA, CB.

Sample Input 2

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 Output 2

64

Sample Input 3

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 Output 3

270274035