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.IOException;
import java.io.InputStream;
import java.util.InputMismatchException;
public class FGlobalRound4 {
	
	public static final long p = 998244353;
	
	public static int N, M;
	public static int[] arr;
	public static int[] inv;
	public static long[][] dp;
	public static int[][] low;

	public static void main(String[] args) {
		FastScanner in = new FastScanner(System.in);
		N = in.nextInt();
		M = in.nextInt();
		
		arr = new int[N];
		inv = new int[N];
		for(int i = 0; i < N; i++) {
			arr[i] = in.nextInt() - 1;
			inv[arr[i]] = i;
		}
		
		low = new int[N+1][N+1];
		for(int i = 0; i < N; i++) {
			int minColor = arr[i];
			for(int j = i + 1; j < N+1; j++)
				low[i][j] = minColor = Math.min(arr[j-1], minColor);
		}
		
		
		dp = new long[N+1][N+1];
		for(int i = 0; i < dp.length; i++)
			for(int j = 0; j < dp[i].length; j++)
				dp[i][j] = -1;
		
		long ans = get(0, N);
		System.out.println(ans);
	}
	
	public static long get(int left, int right) {
		if(right - left <= 1)
			return 1;
		
		long temp = dp[left][right];
		if(temp != -1)
			return temp;
		
		int indexMinColor = getIndexOfMin(left, right);
		
		long leftAns = 0;
		for(int i = left; i <= indexMinColor; i++) {
			long t = (get(left, i) * get(i, indexMinColor)) % p;
			leftAns = (leftAns + t) % p;
		}
		
		long rightAns = 0;
		for(int i = indexMinColor + 1; i <= right; i++) {
			long t = (get(indexMinColor + 1, i) * get(i, right)) % p;
			rightAns = (rightAns + t) % p;
		}
		
		temp = (leftAns * rightAns) % p;
		return dp[left][right] = temp;
	}
	
	public static int getIndexOfMin(int left, int right) {
		int color = low[left][right];
		return inv[color];
	}
	
	
	/**
	 * Source: Matt Fontaine
	 */
	static class FastScanner {
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int chars;

		public FastScanner(InputStream stream) {
			this.stream = stream;
		}

		int read() {
			if (chars == -1)
				throw new InputMismatchException();
			if (curChar >= chars) {
				curChar = 0;
				try {
					chars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (chars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		boolean isEndline(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

		public int nextInt() {
			return Integer.parseInt(next());
		}

		public long nextLong() {
			return Long.parseLong(next());
		}

		public double nextDouble() {
			return Double.parseDouble(next());
		}

		public String next() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public String nextLine() {
			int c = read();
			while (isEndline(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isEndline(c));
			return res.toString();
		}
	}

}
/*
3 3
1 2 3
outputCopy
5
inputCopy
7 7
4 5 1 6 2 3 7
outputCopy
165
*/