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.

if __name__ == '__main__':
    n = int(input())
    aa = list(map(int, input().split()))
    ll,rr = [1]*n,[1]*n
    cl,cr = 1,1
    res = 0
    for il, ir in [(i, n - 1 - i) for i in range(1, n)]:
        cl = (cl + 1) if aa[il-1] < aa[il] else 1
        cr = (cr + 1) if aa[ir] < aa[ir+1] else 1
        res = max(res, cl)
        res = max(res, cr)
        ll[il],rr[ir] = cl,cr
    for i in range(1, n - 1):
        if aa[i-1] < aa[i+1]:
            res = max(res, ll[i-1] + rr[i+1])
    print(res)
        
            
        
        
    
        

