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.

def main():
    buf = input()
    n = int(buf)
    buf = input()
    buflist = buf.split()
    a = list(map(int, buflist))

    sublen_inc = []
    sublen_dec = []
    for i in range(n):
        sublen_inc.append(None)
        sublen_dec.append(None)
    c = 1
    sublen_inc[0] = c
    for i in range(1, n):
        if a[i-1] < a[i]:
            c += 1
        else:
            c = 1
        sublen_inc[i] = c
    c = 1
    sublen_dec[n-1] = c
    for i in range(n-2, -1, -1):
        if a[i] < a[i+1]:
            c += 1
        else:
            c = 1
        sublen_dec[i] = c

    best = max(sublen_inc)
    for i in range(1, n-1):
        if a[i-1] < a[i+1]:
            new_sublen = sublen_inc[i-1] + sublen_dec[i+1]
            if new_sublen > best:
                best = new_sublen

    print(best)

if __name__ == '__main__':
    main()
