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.awt.Point;
import java.math.BigInteger;

public class cf_1178_f {
	
	static long dp[][];
	static int seq[];
	static int ind[][];
	
	public static void main(String[] args) throws Exception {
		FastIO sc = new FastIO(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		
		int N = sc.nextInt();
		int M = sc.nextInt();
		dp = new long[N][N];
		seq = new int[N];
		ind = new int[N][N];
		
		for(int i = 0; i < N; i++) {
			seq[i] = sc.nextInt();
		}
		
		for(int i = 0; i < N; i++) {
			int m = Integer.MAX_VALUE;
			int index = -1;
			
			for(int j = i; j < N; j++) {
				for(int k = i; k <= j; k++) {
					if(seq[k] < m) {
						m = seq[k];
						index = k;
					}
				}
				
				ind[i][j] = index;
			}
		}
		
		for(int i = 0; i < N; i++) {
			for(int j = 0; j < N; j++) {
				dp[i][j] = -1;
			}
		}
		
		pw.println(go(0, N-1));
		pw.close();
	}
	
	static long go(int i, int j) {
		if(dp[i][j] != -1) return dp[i][j];
		
		int mid = ind[i][j];
		long left = 0;
		long right = 0;
		if(mid != i) {
			for(int l = i; l < mid; l++) {
					if(l == i) left += go(i, mid-1);
					else left += go(i, l-1)*go(l, mid-1)%998244353;
					left %= 998244353;
				}
				left += go(i, mid-1);
				left %= 998244353;
		} else left = 1;
		
		if(mid != j) {
			for(int r = mid+1; r <= j; r++) {
					if(r == j) right += go(mid+1, r);
					else right += go(mid+1, r)*go(r+1, j)%998244353;
					right %= 998244353;
				}
				right += go(mid+1, j);
				right %= 998244353;
		} else right = 1;
		
		long ans = left*right%998244353;
		
		return dp[i][j] = ans;
	}
	
	static class FastIO {
		 
		//Is your Fast I/O being bad?
 
		InputStream dis;
		byte[] buffer = new byte[1 << 17];
		int pointer = 0;
 
		public FastIO(String fileName) throws Exception {
			dis = new FileInputStream(fileName);
		}
 
		public FastIO(InputStream is) throws Exception {
			dis = is;
		}
 
		int nextInt() throws Exception {
			int ret = 0;
 
			byte b;
			do {
				b = nextByte();
			} while (b <= ' ');
			boolean negative = false;
			if (b == '-') {
				negative = true;
				b = nextByte();
			}
			while (b >= '0' && b <= '9') {
				ret = 10 * ret + b - '0';
				b = nextByte();
			}
 
			return (negative) ? -ret : ret;
		}
 
		long nextLong() throws Exception {
			long ret = 0;
 
			byte b;
			do {
				b = nextByte();
			} while (b <= ' ');
			boolean negative = false;
			if (b == '-') {
				negative = true;
				b = nextByte();
			}
			while (b >= '0' && b <= '9') {
				ret = 10 * ret + b - '0';
				b = nextByte();
			}
 
			return (negative) ? -ret : ret;
		}
 
		byte nextByte() throws Exception {
			if (pointer == buffer.length) {
				dis.read(buffer, 0, buffer.length);
				pointer = 0;
			}
			return buffer[pointer++];
		}
 
		String next() throws Exception {
			StringBuffer ret = new StringBuffer();
 
			byte b;
			do {
				b = nextByte();
			} while (b <= ' ');
			while (b > ' ') {
				ret.appendCodePoint(b);
				b = nextByte();
			}
 
			return ret.toString();
		}
 
	}
}