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.*;
import java.io.*;
import java.lang.*;
import java.math.*;
public class G {
    public static int[][] index;
    public static void main(String[] args) throws Exception {
        BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
        // int n = Integer.parseInt(bf.readLine());
        StringTokenizer st = new StringTokenizer(bf.readLine());
        int n = Integer.parseInt(st.nextToken());
        int mm = Integer.parseInt(st.nextToken());
        st = new StringTokenizer(bf.readLine());
        int[] b = new int[mm]; for(int i=0; i<mm; i++) b[i] = Integer.parseInt(st.nextToken())-1;
        int counter = 1;
        int m = 1;
        for(int i=1; i<mm; i++) {
          if(b[i] != b[i-1]) m++;
        }
        int[] a = new int[m];
        a[0] = b[0];
        for(int i=1; i<mm; i++) {
          if(b[i] != b[i-1]) {
            a[counter] = b[i];
            counter++;
          }
        }
        if(m > 2 * n) {
          out.println(0);
          out.close();
          System.exit(0);
        }
        int mod = 998244353;

        index = new int[n][2];
        int[] oneIndex = new int[n];
        for(int i=0; i<n; i++) {
          index[i][0] = m+1;
          index[i][1] = -1;

        }
        for(int i=0; i<m; i++) {
          if(i < index[a[i]][0]) index[a[i]][0] = i;
          if(i > index[a[i]][1]) index[a[i]][1] = i;
          oneIndex[a[i]] = i;
        }
        for(int i=n-2; i>=0; i--) {
          for(int j=i+1; j<n; j++) {
            boolean works = false;
            if(index[i][1] < index[j][0]) works = true;
            if(index[i][0] > index[j][1]) works = true;
            if((index[i][0] < index[j][0]) && (index[i][1] > index[j][1])) works = true;
            //if((index[i][0] > index[j][0]) && (index[i][1] < index[j][1])) works = true;
            if(!works) {
              out.println(0);
              out.close();
              System.exit(0);
            }
          }
        }
        int[] depthcount = new int[n];
        int max = -1;
        for(int i=0; i<n; i++) {
          for(int j=0; j<i; j++) {
            if((index[i][0] <= index[j][1]) && (index[j][0] <= index[i][0])) depthcount[i]++;
          }
        }
        ArrayList<ArrayList<Integer>> children = new ArrayList<ArrayList<Integer>>();
        for(int i=0; i<n; i++) children.add(new ArrayList<Integer>());
        ArrayList<Integer> ground = new ArrayList<Integer>();
        int[] parent = new int[n];
        Arrays.fill(parent, -1);
        int[][] sorted = new int[n][2];
        for(int i=0; i<n; i++) {
          sorted[i][0] = index[i][0];
          sorted[i][1] = i;
        }
        Arrays.sort(sorted, new Comparator<int[]>() {
    @Override
    public int compare(int[] o1, int[] o2) {
        return Integer.compare(o1[0], o2[0]);
    }
});

        for(int k=0; k<n; k++) {
            int i = sorted[k][1];
            for(int j=0; j<i; j++) {
              if((index[i][0] <= index[j][1]) && (index[j][0] <= index[i][0]) && (depthcount[i] == depthcount[j]+1)) {
                children.get(j).add(i);
                parent[i] = j;
                break;
              }
            }

          if(parent[i] == -1) ground.add(i);
        }

        long ans = 1;
        for(int par=0; par<n; par++) {
          ans *= getAnsTemp(children.get(par));
          ans %= mod;
        }
        ans *= getAnsTemp(ground);
        ans %= mod;
        out.println(ans);


        out.close(); System.exit(0);
    }
    public static long getAnsTemp(ArrayList<Integer> vals) {
      long ans = 1;
      long mod = 998244353;
      ArrayList<Integer> cur = new ArrayList<Integer>();
      int latest = -1;
      for(int i : vals) {
        if(latest != -1) {
          if(index[latest][1] + 1 != index[i][0]) {
            ans *= getAns(cur);
            ans %= mod;
            cur = new ArrayList<Integer>();
            latest = -1;
          }
        }
        cur.add(i);
        latest = i;
      }
      ans *= getAns(cur);
      ans %= mod;
      return ans;
    }

    public static long getAns(ArrayList<Integer> vals) {

      if(vals.size() == 0) return 1;
      if(vals.size() == 1) return 1;
      int n = vals.size();
      int mod = 998244353;
      int[] a = new int[vals.size()];
      for(int i=0; i<n; i++) a[i] = vals.get(i);
              long[][] dp = new long[n+1][n+1];
              for(int length = 0; length<=n; length++) {
                for(int start = 0; start+length<=n; start++) {
                  if(length==1) dp[start][length] = 1;
                  else if(length == 0) dp[start][length] = 1;
                  else {
                    int min = 10000001;
                    int index = -1;
                    for(int i=start; i<start+length; i++) {
                      if(a[i] < min) {
                        min = a[i];
                        index = i;
                      }
                    }
                    long val1 = 0;
                    for(int i=0; i<=index-start; i++) {
                      val1 += 1L * dp[start][i] * dp[start+i][index-start-i] % mod;
                      val1 %= mod;
                    }
                    long val2 = 0;
                    for(int i=0; i<=start+length-index-1; i++) {
                      val2 += 1L * dp[index+1][i] * dp[index+1+i][start+length-index-1-i] % mod;
                      val2 %= mod;
                    }
                    dp[start][length] = 1L*val1*val2 % mod;
                  }
                }
              }
              return (dp[0][n] % mod);

    }
}