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()))
res = []
first = a[0]
temp = 1
for i in range(1, len(a)):
    if first < a[i]:
        temp += 1
    else:
        res.append((temp, i - 1))
        # print("temp",temp)
        temp = 1
    first = a[i]
if temp >= 1:
    res.append((temp, len(a) - 1))
# print(res)
final_ans = []
for i in range(len(res) - 1):
    l = a[res[i][1]-1]
    l2 = a[res[i][1]]
    f = a[res[i + 1][1] - res[i + 1][0] + 1]
    f2 = a[res[i + 1][1] - res[i + 1][0] + 1]
    if res[i+1][0]>=2:
        f2 = a[res[i + 1][1] - res[i + 1][0] + 2]
    # print(l, f , l2,f2)
    if l < f or l2<f2:
        final_ans.append(res[i][0] + res[i + 1][0] - 1)
    else:
        final_ans.append(max(res[i][0],res[i+1][0]))
# print(final_ans)
if len(final_ans) == 0:
    print(max(res[0]))
else:
    print(max(final_ans))
# if len(res) == 1:
#     print(res[0])
# else:
#
