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:
import sys
input = sys.stdin.readline

n,m=map(int,input().split())
A=list(map(int,input().split()))

A=[a-1 for a in A]

MININDLIST=[[i]*m for i in range(m)]

for i in range(m):
    MIN=A[i]
    MININDNOW=i
    for j in range(i,m):
        if A[j]<MIN:
            MIN=A[j]
            MININDNOW=j

        MININDLIST[i][j]=MININDNOW

mod=998244353

SCORE=[0]*((m+1)**2)

def calc(i,j,m):
    if SCORE[i*(m+1)+j]!=0:
        return SCORE[i*(m+1)+j]
    
    #print(i,j)
    if j==i+1 or i==j:
        return 1
    
    MININD=MININDLIST[i][j-1]

    #print(MININD)

    ANS1=ANS2=0
 
    for mi in range(i,MININD+1):
        ANS1=(ANS1+calc(i,mi,m)*calc(mi,MININD,m))%mod
        
    for Mi in range(MININD+1,j+1):
        ANS2=(ANS2+calc(MININD+1,Mi,m)*calc(Mi,j,m))%mod
 
    SCORE[i*(m+1)+j]=ANS1*ANS2%mod
 
    return SCORE[i*(m+1)+j]
 
print(calc(0,m,m))