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.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.InputMismatchException;
public class FGlobalRound4B {
	
	public static final long p = 998244353;

	public static int[] arr;
	public static int[][] indexLow;
	public static long[][] dp;
	
	public static void main(String[] args) {
		FastScanner in = new FastScanner(System.in);
		int N = in.nextInt();
		int M = in.nextInt();
		arr = new int[M];
		for(int i = 0; i < M; i++)
			arr[i] = in.nextInt() - 1;
		
		arr = compress(arr);
		
		long ans = ans(N, M, arr);
		System.out.println(ans);
	}
	
	public static int[] compress(int[] arr) {
		ArrayList<Integer> list = new ArrayList<>();
		list.add(arr[0]);
		for(int i = 1; i < arr.length; i++)
			if(list.get(list.size() - 1) != arr[i])
				list.add(arr[i]);
		
		int[] temp = new int[list.size()];
		for(int i = 0; i < temp.length; i++)
			temp[i] = list.get(i);
		
		return temp;
	}
	
	public static long ans(int N, int M, int[] arr) {
		if(arr.length > 2 * N)
			return 0;
		
		N = arr.length;
		
		@SuppressWarnings("unchecked")
		ArrayList<Integer>[] positions = new ArrayList[N];
		for(int i = 0; i < N; i++)
			positions[i] = new ArrayList<>();
		
		for(int i = 0; i < arr.length; i++) {
			positions[arr[i]].add(i);
		}
		
		indexLow = new int[N+1][N+1];
		for(int i = 0; i < indexLow.length; i++)
			Arrays.fill(indexLow[i], -1);
		for(int i = 0; i < N; i++) {
			indexLow[i][i+1] = i;
			int min = arr[i];
			for(int j = i + 2; j < N+1; j++) {
				if(arr[j-1] < min) {
					min = arr[j-1];
					indexLow[i][j] = j-1;
				}
				else {
					indexLow[i][j] = indexLow[i][j-1];
				}
			}
		}
		
		dp = new long[arr.length + 1][arr.length + 1];
		for(int i = 0; i < dp.length; i++)
			Arrays.fill(dp[i], -1);
		
		return get(0, arr.length, positions);
	}
	
	public static long get(int left, int right, ArrayList<Integer>[] positions) {
		if(right - left == 0)
			return 1;
		
		if(right - left == 1) {
			ArrayList<Integer> pos = positions[arr[left]];
			if(left <= pos.get(0) && pos.get(pos.size()-1) < right) {
				return 1;
			}
			return 0;
		}
		
		long temp = dp[left][right];
		if(temp != -1) {
			return temp; 
		}
		
		temp = 1;
		int indexMinColor = indexLow[left][right];
		int colorMin = arr[indexMinColor];
		ArrayList<Integer> pos = positions[colorMin];
		int index = Collections.binarySearch(pos, indexMinColor);
		
		if(index != 0 || pos.get(pos.size()-1) >= right) {
			return 0;
		}
		
		long leftAns = 0;
		for(int i = left; i <= indexMinColor; i++) {
			long t = (get(left, i, positions) * get(i, indexMinColor, positions)) % p;
			leftAns = (leftAns + t) % p;
		}
		
		temp = leftAns;
		while(index + 1 < pos.size() && pos.get(index+1) <= right) {
			long t = get(pos.get(index) + 1, pos.get(index+1), positions);
			temp = (temp * t) % p;
			index++;
		}
		
		long rightAns = 0;
		indexMinColor = pos.get(index);
		for(int i = indexMinColor + 1; i <= right; i++) {
			long t = (get(indexMinColor + 1, i, positions) * get(i, right, positions)) % p;
			rightAns = (rightAns + t) % p;
		}
		
		temp = (temp * rightAns) % p;
		
		return dp[left][right] = temp;
	}
	
	/**
	 * 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
2 3
1 2 1
outputCopy
1
inputCopy
2 3
2 1 2
outputCopy
0
inputCopy
7 7
4 5 1 6 2 3 7
outputCopy
165
inputCopy
8 17
1 3 2 2 7 8 2 5 5 4 4 4 1 1 6 1 1
outputCopy
20
*/