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.
import sys

# inf = open('input.txt', 'r')
# reader = (line.rstrip() for line in inf)
reader = (line.rstrip() for line in sys.stdin)
input = reader.__next__

n = int(input())
a = list(map(int, input().split()))
segm = []
st = 0
for i in range(1, n):
    if a[i-1] >= a[i]:
        if i-1 > st:
            segm.append((st, i-1))
        st = i
if n-1 > st:
    segm.append((st, n-1))
if not segm:
    print(1)
    sys.exit()
elif len(segm) == 1:
    print(segm[0][1] - segm[0][0] + 1)
    sys.exit()
    
maxSegm = max(segm, key=lambda x: x[1] - x[0])
currMax = maxSegm[1] - maxSegm[0] + 1
for i in range(len(segm)):
    st0, en0 = segm[i-1]
    st1, en1 = segm[i]
    if en0 + 2 == st1 and a[en0] < a[st1]:
        currMax = max(currMax, en1 - st0)
    elif en0 + 1 == st1 and (a[en0] < a[st1+1] or a[en0-1] < a[st1]):
        currMax = max(currMax, en1 - st0)
    
print(currMax)

# inf.close()