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 PYTHON3):

Solution:
def main():

    line = input().split()
    n = int(line[0])

    line = input().split()

    v = [int(x) for x in line]

    mod = 998244353

    dp = [[1] * (n + 5) for i in range(n + 5)]

    for sz in range(2, n + 1):
        for lo in range(1, n - sz + 2):
            hi = lo + sz - 1

            pos, num = -1, n + 5
            
            for k in range(lo, hi + 1):
                if v[k - 1] < num:
                    num = v[k - 1]
                    pos = k
            
            s1, s2 = 0, 0

            for k in range(lo, pos + 1):
                cnt = dp[lo][k - 1] * dp[k][pos - 1] % mod
                s1 = (s1 + cnt) % mod
            
            for k in range(pos, hi + 1):
                cnt = dp[pos + 1][k] * dp[k + 1][hi] % mod
                s2 = (s2 + cnt) % mod

            dp[lo][hi] = s1 * s2 % mod

    print(dp[1][n])


main()