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.
from sys import stdin

read = stdin.readline

def main():
    n = int(read())
    nums = list(map(int, read().strip().split()))

    inclass, ac, edges, cnt = dict(), 1, list(), 0
    for num in nums: inclass[num] = 0
    for i in range(len(nums)-1):
        if nums[i+1] > nums[i]: ac+=1
        else:
            ac_temp = ac-1
            inclass[nums[i]] = (ac, cnt)
            j = i-1
            while ac_temp > 0: inclass[nums[j]] = (ac, cnt); j-=1; ac_temp -= 1;
            ac = 1
            edges.append(i+1)
            cnt += 1
    i = len(nums)-1
    ac_temp = ac-1
    inclass[nums[i]] = (ac, cnt)
    j = i-1
    while ac_temp > 0: inclass[nums[j]] = (ac, cnt); j-=1; ac_temp -= 1;
    ac = 1

    ans = 0
    for key in inclass: ans = max(ans, inclass[key][0])
    for i in range(1, len(nums)-1):
        if nums[i-1] < nums[i+1] and inclass[nums[i-1]][1] != inclass[nums[i+1]][1]:
            ans = max(ans, inclass[nums[i-1]][0]+inclass[nums[i+1]][0]-1)
    print(ans)

main()