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.*;
 
public class Main {
	public static void main(String args[]) {new Main().work();}
	
	Scanner in = new Scanner(System.in);
	PrintWriter out = new PrintWriter(System.out);
	int mod=998244353;
	void work() {		
		int n=in.nextInt();
		int m=in.nextInt();
		
		int[] A=new int[n];
		for(int i=0;i<n;i++) A[i]=in.nextInt();
		long[][] dp=new long[n][n];
		out.print(helper(A,0,n-1,dp));
		out.flush();
	}
	
	long helper(int[] A,int s,int e,long[][] dp){
	    if(s>e) return 1;
	    if(dp[s][e]>0) return dp[s][e];
	    int min=s;
	    for(int i=s;i<=e;i++){
	        if(A[i]<A[min]){
	            min=i;
	        }
	        dp[s][e]+=((helper(A,s,min-1,dp)*helper(A,min+1,i,dp)%mod)*helper(A,i+1,e,dp))%mod;
	    }
	    dp[s][e]%=mod;
	    return dp[s][e];
	}
}