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>
const int N = 1e3 + 5, M = 1e6 + 5;
const int MOD = 998244353;
int n, m, a[M], f[N][N];
std::vector<int> vec[N];
void add(int &x, int y) { (x += y) >= MOD && (x -= MOD); }
int main() {
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= m; i++) scanf("%d", &a[i]);
  m = std::unique(a + 1, a + m + 1) - (a + 1);
  if (m > 2 * n) {
    printf("0\n");
    return 0;
  }
  for (int i = 1; i <= m; i++) vec[a[i]].emplace_back(i);
  for (int i = 1; i <= m + 1; i++) f[i][i - 1] = 1;
  for (int l = 1; l <= m; l++) {
    for (int i = 1, j = l; j <= m; i++, j++) {
      int c = *std::min_element(a + i, a + j + 1);
      int x = vec[c].front(), y = vec[c].back();
      if (x < i || y > j) {
        f[i][j] = 0;
        continue;
      }
      int L = 0, R = 0;
      for (int k = i; k <= x; k++) {
        add(L, 1LL * f[i][k - 1] * f[k][x - 1] % MOD);
      }
      for (int k = y; k <= j; k++) {
        add(R, 1LL * f[y + 1][k] * f[k + 1][j] % MOD);
      }
      f[i][j] = 1LL * L * R % MOD;
      for (int k = 1; k < (int)vec[c].size(); k++) {
        if (vec[c][k - 1] + 1 < vec[c][k]) {
          f[i][j] = 1LL * f[i][j] * f[vec[c][k - 1] + 1][vec[c][k] - 1] % MOD;
        }
      }
    }
  }
  printf("%d\n", f[1][m]);
  return 0;
}