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;
using ll = long long;
using vi = vector<int>;
const int MAX = 1010;
int c[MAX];
int p[MAX];
ll res[MAX][MAX];
const int MOD = 998244353;
void nope() {
  printf("0\n");
  exit(0);
}
int main() {
  int n, m;
  scanf("%d %d", &n, &m);
  for (int i = 1; i <= m; i++) {
    scanf("%d", &c[i]);
    p[c[i]] = i;
  }
  for (int j = 0; j < m; j++) {
    for (int i = 1; i + j <= m; i++) {
      if (j == 0) {
        res[i][j] = 1;
        continue;
      }
      int mini = m;
      for (int k = i; k <= i + j; k++) {
        mini = min(mini, c[k]);
      }
      if (p[mini] == i) {
        for (int pos = i + 1; pos < i + j; pos++) {
          res[i][j] = (res[i][j] + res[i + 1][pos - i - 1] *
                                       res[pos + 1][i + j - pos - 1]) %
                      MOD;
        }
        res[i][j] = (res[i][j] + 2 * res[i + 1][j - 1]) % MOD;
        continue;
      }
      if (p[mini] == i + j) {
        for (int pos = i + j - 1; pos > i; pos--) {
          res[i][j] =
              (res[i][j] + res[i][pos - 1 - i] * res[pos][i + j - 1 - pos]) %
              MOD;
        }
        res[i][j] = (res[i][j] + 2 * res[i][j - 1]) % MOD;
        continue;
      }
      res[i][j] = (res[i][p[mini] - i] * res[p[mini]][i + j - p[mini]]) % MOD;
    }
  }
  printf("%lld\n", res[1][m - 1]);
}