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;
int a[501];
long long f[502][501];
int id[501];
int mn[501][501];
int n, m, i, j, k, l, s, len;
long long s1, s2;
int main() {
  scanf("%d%d", &n, &m);
  for (i = 1; i <= m; i++) {
    scanf("%d", &a[i]);
    id[a[i]] = i;
  }
  for (i = 1; i <= m; i++) {
    mn[i][i] = a[i];
    for (j = i + 1; j <= m; j++)
      mn[i][j] = (mn[i][j - 1] < a[j] ? mn[i][j - 1] : a[j]);
  }
  f[1][0] = 1;
  for (i = 1; i <= m; i++) {
    f[i][i] = 1;
    f[i + 1][i] = 1;
  }
  for (len = 2; len <= m; len++) {
    for (i = 1; i <= m - len + 1; i++) {
      j = i + len - 1;
      s = id[mn[i][j]];
      s1 = 0;
      s2 = 0;
      for (k = i; k <= s; k++)
        s1 = (s1 + f[i][k - 1] * f[k][s - 1] % 998244353) % 998244353;
      for (l = s; l <= j; l++)
        s2 = (s2 + f[s + 1][l] * f[l + 1][j] % 998244353) % 998244353;
      f[i][j] = (f[i][j] + s1 * s2 % 998244353) % 998244353;
    }
  }
  printf("%I64d\n", f[1][m]);
}