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 PYTHON):

Solution:
import sys
range = xrange
input = raw_input

MOD = 998244353 

m,n = [int(x) for x in input().split()]
C = [int(x) - 1 for x in input().split()]

C2 = [C[0]]
for c in C:
    if C2[-1] != c: 
        C2.append(c)
C = C2
n = len(C)

if n > 2*m:
    print 0
    sys.exit()

pos = [[] for _ in range(n)]
for i in range(n):
    pos[C[i]].append(i)


DP = [[1]*(n + 1) for _ in range(n + 1)]
for le in range(1, n + 1):
    for i in range(n - le + 1):
        j = i + le
        k1 = min(range(i,j), key = C.__getitem__)
        c = C[k1]

        k1 = pos[c][0]
        k2 = pos[c][-1]

        ans1 = 0
        for split in range(i,k1 + 1):
            ans1 += DP[i][split] * DP[split][k1] % MOD   
        
        ans2 = 0
        for split in range(k2+1, j + 1):
            ans2 += DP[k2 + 1][split] * DP[split][j] % MOD

        posc = pos[c]
        for ind in range(len(posc) - 1):
            ans1 = (ans1 * DP[posc[ind] + 1][posc[ind + 1]] % MOD)

        DP[i][j] = int((ans1 % MOD) * (ans2 % MOD) % MOD)

print DP[0][n]