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 col[505];
pair<int, int> mn[505][505];
pair<int, int> min(pair<int, int> a, pair<int, int> b) {
  if (a.first < b.first) return a;
  return b;
}
long long memo[505][505];
long long dp(int l, int r) {
  if (l == r) return 1;
  if (memo[l][r] != -1) return memo[l][r];
  int m = mn[l][r].second;
  long long lft;
  if (l <= m - 1)
    lft = dp(l, m - 1) * 2 % 998244353;
  else
    lft = 1;
  for (int i = (l); i <= (m - 2); i++) {
    lft = (lft + dp(l, i) * dp(i + 1, m - 1) % 998244353) % 998244353;
  }
  long long rgt;
  if (m + 1 <= r)
    rgt = dp(m + 1, r) * 2 % 998244353;
  else
    rgt = 1;
  for (int i = (m + 2); i <= (r); i++) {
    rgt = (rgt + dp(m + 1, i - 1) * dp(i, r)) % 998244353;
  }
  return memo[l][r] = lft * rgt % 998244353;
}
int main() {
  int n, m;
  scanf("%d %d", &n, &m);
  for (int i = (1); i <= (m); i++) scanf("%d", &col[i]);
  for (int i = (1); i <= (m); i++) {
    mn[i][i] = {col[i], i};
    for (int j = (i + 1); j <= (m); j++) {
      mn[i][j] = min(mn[i][j - 1], {col[j], j});
    }
  }
  memset(memo, -1, sizeof(memo));
  printf("%d\n", dp(1, m));
  return 0;
}