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;
inline int gi() {
  int f = 1, x = 0;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -f;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') x = x * 10 + ch - '0', ch = getchar();
  return f * x;
}
const int N = 505, P = 998244353;
int n, m, c[N];
int dp[N][N], pos[N];
int f(int l, int r) {
  if (~dp[l][r]) return dp[l][r];
  if (l >= r) return dp[l][r] = 1;
  for (int i = (1); i <= (n); ++i)
    if (pos[i] >= l && pos[i] <= r) {
      int mid = pos[i], lf = 0, rg = 0;
      for (int L = (l); L <= (mid); ++L)
        (lf += (long long)f(l, L - 1) * f(L, mid - 1) % P) %= P;
      for (int R = (mid); R <= (r); ++R)
        (rg += (long long)f(mid + 1, R) * f(R + 1, r) % P) %= P;
      dp[l][r] = (long long)lf * rg % P;
      return dp[l][r];
    }
}
int main() {
  memset(dp, -1, sizeof(dp));
  n = gi(), m = gi();
  for (int i = (1); i <= (n); ++i) c[i] = gi(), pos[c[i]] = i;
  printf("%d\n", f(1, n));
  return 0;
}