You are given an array a consisting of n integers.

You can remove at most one element from this array. Thus, the final length of the array is n-1 or n.

Your task is to calculate the maximum possible length of the strictly increasing contiguous subarray of the remaining array.

Recall that the contiguous subarray a with indices from l to r is a[l ... r] = a_l, a_{l + 1}, ..., a_r. The subarray a[l ... r] is called strictly increasing if a_l < a_{l+1} < ... < a_r.

Input

The first line of the input contains one integer n (2 ≤ n ≤ 2 ⋅ 10^5) — the number of elements in a.

The second line of the input contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9), where a_i is the i-th element of a.

Output

Print one integer — the maximum possible length of the strictly increasing contiguous subarray of the array a after removing at most one element.

Examples

Input


5
1 2 5 3 4


Output


4


Input


2
1 2


Output


2


Input


7
6 5 4 3 2 4 3


Output


2

Note

In the first example, you can delete a_3=5. Then the resulting array will be equal to [1, 2, 3, 4] and the length of its largest increasing subarray will be equal to 4.



n=int(input())



dp=[[0,0] for i in range(n)]


dp[0]=[1,1]

t= list(map(int,input().split()))



for j in range(1,n):

    if t[j]>t[j-1]:
        dp[j][0]= dp[j-1][0]+1
        dp[j][1]= dp[j-1][1]+1
    else:
        dp[j][0]=1
        dp[j][1] = 1

    if j>=2 and t[j]>t[j-2]:
        dp[j][1]=max(dp[j][1] ,  dp[j-2][0]+1)


ans = 0

for i in dp:
    ans=max(ans, max(i))
print(ans)

