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 process(A):
    answer = 1
    n = len(A)
    current = [[A[0], A[0], 0, 0]]
    for i in range(1, n):
        if A[i] <= current[-1][1]:
            answer = max(answer, current[-1][3]-current[-1][2]+1)
            current.append([A[i], A[i], i, i])
        else:
            current[-1][1] = A[i]
            current[-1][3] = i
    answer = max(answer, current[-1][3]-current[-1][2]+1)
  #  print(current)
    m = len(current)
    for i in range(m-1):
        s1, e1, i1, i2 = current[i]
        s2, e2, j1, j2 = current[i+1]
        if i2 > 0 and A[i2-1] < A[j1]:
            answer = max(answer, j2-j1+i2-i1+1)
        if j1 < j2 and A[i2] < A[j1+1]:
            answer = max(answer, j2-j1+i2-i1+1)
    for i in range(m-2):
        s1, e1, i1, i2 = current[i]
        s2, e2, j1, j2 = current[i+1]
        s3, e3, k1, k2 = current[i+2]
        if j1==j2 and A[i2] < A[k1]:
            answer= max(answer, k2-k1+1+i2-i1+1)
    return answer

n = int(input())
A = [int(x) for x in input().split()]
print(process(A))