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.
def play(arr):
    n = len(arr)
    if n == 1:
        return 1
    l = [0] * n
    r = [0] * n
    s= 0
    for i in range(1, n):
        if arr[i] > arr[i - 1]:
            s += 1
            l[i] = s
        else:
            s += 1
            l[i] = s
            s = 0     

    s = 0
    for i in range(n - 2, -1, -1):
        if arr[i + 1] > arr[i]:
            s += 1
            r[i] = s
        else:
            s += 1
            r[i] = s
            s = 0     

    m = 1
    for i in range(0, n):           
        if i > 0:
            if i < n - 1:
                if arr[i - 1] >= arr[i + 1]:
                    if arr[i] > arr[i - 1]:
                        m = max(m, l[i] + 1)
                    
                    if arr[i] < arr[i + 1]:
                        m = max(m, r[i] + 1)                    
                    
                    m = max(m, l[i], r[i])
                elif arr[i] > arr[i - 1] and arr[i] < arr[i + 1]:
                    m = max(m, l[i] + r[i] + 1)
                else:
                    m = max(m, l[i] + r[i])
            elif arr[i] > arr[i - 1]:
                m = max(m, l[i] + 1)
            else:
                m = max(m, l[i])
        elif arr[i] < arr[i + 1]:
            m = max(m, r[i] + 1)
        else:
            m = max(m, r[i])            
    return m

def main():
    n =  list(map(int, input().split()))[0]

    arr = list(map(int, input().split()))
    print(play(arr))
    
main()
# print(play([1,2,5,3,4]))
# print(play([1,2]))
# print(play([6,5,4,3,2,4,3]))
# print(play([1,5,1]))
# print(play([1,2,2,3,5,4,6,7]))
# print(play([2,1]))
# print(play([1, 2, 5, 6, 5, 6, 7]))
# print(play([1, 2, 6, 1, 2]))

# print(play([1, 2, 2, 1, 2, 3]))
# print(play([1, 2, 0, 3, 4, 5]))
