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combinatorics

dp

fft

math

*2700

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G. String Counting

time limit per test

10 secondsmemory limit per test

1024 megabytesinput

standard inputoutput

standard outputYou have $$$c_1$$$ letters 'a', $$$c_2$$$ letters 'b', ..., $$$c_{26}$$$ letters 'z'. You want to build a beautiful string of length $$$n$$$ from them (obviously, you cannot use the $$$i$$$-th letter more than $$$c_i$$$ times). Each $$$c_i$$$ is greater than $$$\frac{n}{3}$$$.

A string is called beautiful if there are no palindromic contiguous substrings of odd length greater than $$$1$$$ in it. For example, the string "abacaba" is not beautiful, it has several palindromic substrings of odd length greater than $$$1$$$ (for example, "aca"). Another example: the string "abcaa" is beautiful.

Calculate the number of different strings you can build, and print the answer modulo $$$998244353$$$.

Input

The first line contains one integer $$$n$$$ ($$$3 \le n \le 400$$$).

The second line contains $$$26$$$ integers $$$c_1$$$, $$$c_2$$$, ..., $$$c_{26}$$$ ($$$\frac{n}{3} < c_i \le n$$$).

Output

Print one integer — the number of strings you can build, taken modulo $$$998244353$$$.

Examples

Input

4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

Output

422500

Input

3 2 2 2 2 2 2 3 3 3 2 2 2 2 2 2 3 3 3 2 2 3 2 2 3 2 2

Output

16900

Input

400 348 322 247 158 209 134 151 267 268 176 214 379 372 291 388 135 147 304 169 149 193 351 380 368 181 340

Output

287489790

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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