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.io.*;
import java.lang.reflect.Array;
import java.util.*;

public class Main {
    static int inf = 998244353;
    public static void main(String[] args) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        pw = new PrintWriter(System.out);
        int n = nextInt();
        int m = nextInt();
        int mod = inf;
        int c[] = new int [n];
        for(int i = 0;i < n;i++) c[i] = nextInt();
        long dp[][] = new long [n][n];
        for(int i = 0;i < n;i++) {
            for(int j = 0;j < n;j++) dp[i][j] = 1;
        }
        for(int len = 2;len <= n;len++) {
            for(int l = 0;l < n;l++) {
                int r = (l + len - 1);
                if (r >= n) break;
                int id = -1;
                int min = inf;
                for(int i = l;i <= r;i++) {
                    if (min > c[i]) {
                        min = c[i];
                        id = i;
                    }
                }
                long left = 0;
                for(int i = l;i <= id;i++) {
                    int i1 = Math.max(i - 1, l);
                    int id1 = Math.max(id - 1, i);
                    left += (dp[l][i1] * dp[i][id1]) % mod;
                }
                left %= mod;
                dp[l][r] = 0;
                for(int i = id;i <= r;i++) {
                    int i1 = Math.min(i + 1, r);
                    int id1 = Math.min(id + 1, i);
                    long right = (dp[id1][i] * dp[i1][r]) % mod;
                    dp[l][r] = (dp[l][r] + right * left) % mod;
                }
            }
        }
        pw.println(dp[0][n - 1]);
        pw.close();
    }

    static BufferedReader br;

    static StringTokenizer st = new StringTokenizer("");
    static PrintWriter pw;
    /*static String next() throws IOException {
        int c = br.read();
        while (Character.isWhitespace(c)) c = br.read();
        StringBuilder sb = new StringBuilder();
        while (!Character.isWhitespace(c)) {
            sb.appendCodePoint(c);
            c = br.read();
        }
        return sb.toString();
    }*/

    static String next() throws IOException {
        if (!st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
        return st.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    static Double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }
}

class pair {
    int x, y;
    pair(int a, int b) {
        x = a;
        y = b;
    }
    pair() {}
}