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())
arr = list(map(int, input().split()))
inc = []
count = 1
start = 0
if len(arr) == 1:
    print(1)
else:
    for i in range(1, len(arr)):
        if arr[i] > arr[i - 1]:
            count += 1
        else:
            if i - start != 1:
                inc.append([start, i-1, i-start])
            start = i
            count = 0
    if i-start+1 > 1:
        inc.append([start, i, i - start + 1])
    if inc:
        m = inc[0][2]
    else:
        m = 1
    for i in range(1, len(inc)):
        if (inc[i][0] - inc[i-1][1] - 1) == 1:
            if arr[inc[i][0]] > arr[inc[i-1][1]]:
                m = max(m, inc[i][2] + inc[i-1][2])
        else:
            if (inc[i][0] - inc[i-1][1] - 1) == 0:
                if arr[inc[i][0]] > arr[inc[i - 1][1] - 1]:
                    m = max(m, inc[i][2] + inc[i - 1][2] - 1)
                elif arr[inc[i][0] + 1] > arr[inc[i - 1][1]]:
                    m = max(m, inc[i][2] + inc[i - 1][2] - 1)
        m = max(m, inc[i][2])
    print(m)
