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()))

inc = []
curinc = 1
curincmax = []
gap = 0
gaps = []
maxinc = 1
for i in range(1, n):
    #print(i, a[i] > a[i-1])
    if a[i] > a[i-1]:
        if gap > 0:
            #print(gap, i)
            if gap == 1 and a[i-1] > a[i-3]:
                #print(i, a[i])
                gaps.append(len(inc))
            gap = 0
        curinc += 1
    else:
        #print(curinc, i)
        gap += 1
        inc.append(curinc)
        maxinc = max(curinc, maxinc)
        curinc = 1


inc.append(curinc)
maxinc = max(curinc, maxinc)
#print(inc, maxinc)
total = 0
special = 0
for e in range(len(inc)):
    each = inc[e]
    total += each
    if total+1 < n and a[total-1] < a[total+1]:
        special = max(special, inc[e]+inc[e+1]-1)
    elif total-2 >= 0 and total < n and a[total-2] < a[total]:
        special = max(special, inc[e]+inc[e+1]-1)

print(max(special, maxinc))