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.
# Contest: Codeforces Round #605 (Div. 3) (https://codeforces.com/contest/1272)
# Problem: D: Remove One Element (https://codeforces.com/contest/1272/problem/D)

def rint():
    return int(input())


def rints():
    return list(map(int, input().split()))


n = rint()
a = rints()
rng = []
l = 0
for i in range(1, len(a)):
    if a[i] <= a[i - 1]:
        rng.append((l, i))
        l = i
rng.append((l, n))
mx = max(r - l for l, r in rng)
for i in range(len(rng) - 1):
    l1, r1 = rng[i]
    l2, r2 = rng[i + 1]
    if r1 - l1 == 1 or r2 - l2 == 1:
        continue
    if a[r1 - 2] < a[l2] or a[r1 - 1] < a[l2 + 1]:
        mx = max(mx, r2 - l1 - 1)
print(mx)
