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 JAVA):

Solution:
import java.util.Scanner;

//https://codeforces.com/contest/1178/problem/F1
public class ShortColorfulStrip {
    private static long[][] dp;
    private static int[][] minInd;
    private static long MOD = 998244353L;

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m = sc.nextInt();
        int[] a = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = sc.nextInt();
        }
        int[][] min = new int[n][n];
        minInd = new int[n][n];
        for (int i = 0; i < n; i++) {
            min[i][i] = a[i];
            minInd[i][i] = i;
            for (int j = i + 1; j < n; j++) {
                if (a[j] < min[i][j - 1]) {
                    min[i][j] = a[j];
                    minInd[i][j] = j;
                } else {
                    min[i][j] = min[i][j - 1];
                    minInd[i][j] = minInd[i][j - 1];
                }
            }
        }
        dp = new long[n][n];
        System.out.println(solve(0, n - 1));
    }

    private static long solve(int stInd, int endInd) {
        if (endInd < stInd) {
            return 1;
        }
        if (dp[stInd][endInd] != 0) {
            return dp[stInd][endInd];
        }
        int mid = minInd[stInd][endInd];
        long lowWays = 0;
        for (int j = stInd - 1; j < mid; j++) {
            lowWays = (lowWays + solve(stInd, j) * solve(j + 1, mid - 1)) % MOD;
        }
        long highWays = 0;
        for (int j = mid; j <= endInd; j++) {
            highWays = (highWays + solve(mid + 1, j) * solve(j + 1, endInd)) % MOD;
        }
        long ways = (lowWays * highWays) % MOD;
        dp[stInd][endInd] = ways;
        return dp[stInd][endInd];
    }
}