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())
a = list(map(int, input().split()))
dp = [[a[0]]]
for i in range(1, n):
    if a[i] > a[i - 1]:
        dp[-1].append(a[i])
    else:
        dp.append([a[i]])
maxm = 1
for x in dp:
    maxm = max(maxm, len(x))
m = len(dp)
# print(dp)
for i in range(m):
    if len(dp[i]) == 1:
        if i + 1 < m and i - 1 >= 0 and dp[i + 1][0] > dp[i - 1][-1]:
            maxm = max(len(dp[i - 1] + dp[i + 1], maxm))
    else:
        if i > 0 and dp[i - 1][-1] < dp[i][1]:
            maxm = max(maxm, len(dp[i - 1]) + len(dp[i]) - 1)
        if i + 1 < m and dp[i][-2] < dp[i + 1][0]:
            maxm = max(maxm, len(dp[i]) + len(dp[i + 1]) - 1)
print(maxm)