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.
import sys
input = sys.stdin.readline


N = int(input())
A = list(map(int, input().split()))

pre = -1
P = []
tmp = 0
for i,a in enumerate(A):
    if a > pre:
        P.append(tmp)
    else:
        tmp = i
        P.append(i)
    pre = a

Q = [-1]*N
tmp = N-1
pre = N-1
for i in reversed(range(N)):
    a = A[i]
    if a < pre:
        Q[i] = tmp
    else:
        tmp = i
        Q[i] = tmp
    pre = a

ans = max(Q[0]+1, N-P[N-1])
for i in range(1, N-1):
    ans = max(ans, Q[i]-P[i]+1)
    if A[i-1] < A[i+1]:
        ans = max(ans, Q[i+1]-P[i-1])
print(ans)