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())) 

increasing = [1]*N 
for i in range (1, N):
    if A[i] > A[i-1]: 
        increasing[i] = increasing[i-1] + 1 

decreasing = [1]*N 
for i in range (N-2, -1, -1): 
    if A[i] < A[i+1]: 
        decreasing[i] = decreasing[i+1] + 1 

afterRem = [1]*N  
for i in range (N): 
    try: 
        l = increasing [i-1] 
        if i == 0 : 
            raise IndexError 
    except IndexError: 
        l = 0 
    try: 
        r = decreasing [i+1] 
    except IndexError: 
        r = 0 

    # print (l,r) 
    try: 
        if i>0 and A[i-1] < A[i+1]: 
            afterRem[i] = l+r 
        else: 
            afterRem[i] = max (l,r) 
    except IndexError: 
        afterRem[i] = max (l, r)   

print (max(max(increasing), max(afterRem)))  
# print (increasing, decreasing) 
# print (afterRem) 