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;
long long n, m, a[505], dp[505][505];
long long fun(long long l, long long r) {
  if (l >= r) return 1;
  if (dp[l][r] != -1) return dp[l][r];
  long long x = find(a + l, a + r + 1, *min_element(a + l, a + r + 1)) - a;
  long long ans = 0, y = 0;
  for (__typeof((r + 1)) i = (x); i < (r + 1); i++)
    y = ((y) % 998244353 +
         ((((fun(x + 1, i)) % 998244353) * ((fun(i + 1, r)) % 998244353)) %
          998244353) %
             998244353) %
        998244353;
  for (__typeof((x + 1)) i = (l); i < (x + 1); i++)
    ans =
        ((ans) % 998244353 +
         ((((fun(l, i - 1)) % 998244353) *
           (((((fun(i, x - 1)) % 998244353) * ((y) % 998244353)) % 998244353) %
            998244353)) %
          998244353) %
             998244353) %
        998244353;
  dp[l][r] = ans;
  return ans;
}
void solve() {
  cin >> n >> m;
  for (__typeof((n + 1)) i = (1); i < (n + 1); i++) cin >> a[i];
  memset(dp, -1, sizeof dp);
  {
    cout << fun(1, n) << "\n";
    return;
  };
}
void prep() {}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  long long t = 1;
  prep();
  cout << fixed << setprecision(12);
  while (t--) solve();
  return 0;
}