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 n, a[507], p[507], m;
long long f[507][507], lows[507][507];
int main() {
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= n; i++)
    scanf("%d", &a[i]), p[a[i]] = i, lows[i][i] = a[i];
  for (int i = 1; i <= n; i++)
    for (int j = i + 1; j <= n; j++)
      lows[i][j] = min(lows[i][j - 1], 1ll * a[j]);
  for (int i = 0; i <= n + 1; i++)
    for (int j = 0; j <= n + 1; j++) f[i][j] = 1;
  for (int i = 1; i <= n; i++) {
    for (int l = 1; l + i - 1 <= n; l++) {
      int r = l + i - 1;
      int low = lows[l][r];
      int pos = p[low];
      long long w1 = 0, w2 = 0;
      for (int l1 = l; l1 <= pos; l1++)
        w1 = (w1 + f[l][l1 - 1] * f[l1][pos - 1] % 998244353) % 998244353;
      for (int r1 = pos; r1 <= r; r1++)
        w2 = (w2 + f[pos + 1][r1] * f[r1 + 1][r] % 998244353) % 998244353;
      if (!w1) w1 = 1;
      if (!w2) w2 = 1;
      f[l][r] = w1 * w2 % 998244353;
    }
  }
  cout << f[1][n] % 998244353 << endl;
  return 0;
}