Problem: This is the first subtask of problem F. The only differences between this and the second subtask are the constraints on the value of m and the time limit. You need to solve both subtasks in order to hack this one.

There are n+1 distinct colours in the universe, numbered 0 through n. There is a strip of paper m centimetres long initially painted with colour 0. 

Alice took a brush and painted the strip using the following process. For each i from 1 to n, in this order, she picks two integers 0 ≤ a_i < b_i ≤ m, such that the segment [a_i, b_i] is currently painted with a single colour, and repaints it with colour i. 

Alice chose the segments in such a way that each centimetre is now painted in some colour other than 0. Formally, the segment [i-1, i] is painted with colour c_i (c_i ≠ 0). Every colour other than 0 is visible on the strip.

Count the number of different pairs of sequences \\{a_i\}_{i=1}^n, \\{b_i\}_{i=1}^n that result in this configuration. 

Since this number may be large, output it modulo 998244353.

Input

The first line contains a two integers n, m (1 ≤ n ≤ 500, n = m) — the number of colours excluding the colour 0 and the length of the paper, respectively.

The second line contains m space separated integers c_1, c_2, …, c_m (1 ≤ c_i ≤ n) — the colour visible on the segment [i-1, i] after the process ends. It is guaranteed that for all j between 1 and n there is an index k such that c_k = j.

Note that since in this subtask n = m, this means that c is a permutation of integers 1 through n.

Output

Output a single integer — the number of ways Alice can perform the painting, modulo 998244353.

Examples

Input


3 3
1 2 3


Output


5


Input


7 7
4 5 1 6 2 3 7


Output


165

Note

In the first example, there are 5 ways, all depicted in the figure below. Here, 0 is white, 1 is red, 2 is green and 3 is blue.

<image>

Below is an example of a painting process that is not valid, as in the second step the segment 1 3 is not single colour, and thus may not be repainted with colour 2.

<image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const long long N = 505, M = 998244353;
long long n, m, a[N], b[N], f[N][N], Min[N][N];
signed main() {
  scanf("%lld%lld", &n, &m);
  for (long long i = 1; i <= n; i++) scanf("%lld", &a[i]), b[a[i]] = i;
  for (long long i = 1; i <= n; i++) {
    Min[i][i] = a[i];
    for (long long j = i + 1; j <= n; j++) Min[i][j] = min(Min[i][j - 1], a[j]);
  }
  for (long long i = 0; i < N; i++)
    for (long long j = 0; j < N; j++) f[i][j] = 1;
  for (long long i = n; i; i--)
    for (long long j = i + 1; j <= n; j++) {
      long long P = b[Min[i][j]], l = 0, r = 0;
      for (long long k = i; k <= P; k++) (l += f[i][k - 1] * f[k][P - 1]) %= M;
      for (long long k = P; k <= j; k++) (r += f[P + 1][k] * f[k + 1][j]) %= M;
      f[i][j] = l * r % M;
    }
  printf("%lld\n", f[1][n]);
}