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 fractions import gcd
# from datetime import date, timedelta
from heapq import*
import math
from collections import defaultdict, Counter, deque
from bisect import *
import itertools
import sys
sys.setrecursionlimit(10 ** 7)
MOD = 10 ** 9 + 7
# input = sys.stdin.readline

def main():
    n = int(input())
    a = list(map(int, input().split()))
    
    l = []
    ind = []
    s = a[0]
    c = 1
    for i in range(1, n):
        if s < a[i]:
            c += 1
        else:
            l.append(c)
            ind.append(i - 1)
            c = 1
        s = a[i]
    l.append(c)
    ind.append(i)
    ans = max(l)
    for i in range(len(ind)-1):
        j = ind[i]
        if j + 1 < n and a[j - 1] < a[j + 1]:
            ans = max(ans, l[i] + l[i + 1] - 1)
        if j + 2 < n and a[j] < a[j + 2]:
            ans = max(ans, l[i] + l[i + 1] - 1)

    print(ans)


if __name__ == '__main__':
    main()
