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

def rl():
    return sys.stdin.readline()

def compute(A,N):
    A.append(0)
    st = 0
    n = A[0]
    l = []
    for i,v in enumerate(A[1:]):
        #print(i,v)
        if v <= n:
            l.append((st,i))
            st = i+1
        n = v
    
    #print(l)
    max1 = l[0][1] - l[0][0] + 1
    for i in range(1,len(l)):
        if l[i][0] - l[i-1][1] == 1:
            if ((l[i][1] - l[i][0]+1) > 1 and A[l[i][0]+1] > A[l[i-1][1]]) or ((l[i-1][1] - l[i-1][0]+1) > 1 and A[l[i][0]] > A[l[i-1][1]-1]):
                c = l[i][1] - l[i-1][0] 
            else:
                c = l[i][1] - l[i][0] + 1
        else:
            c = l[i][1] - l[i][0] + 1
        #if max1<c:
        max1 = max(max1,c)
            #print(l[i],l[i-1],max1,A[l[i-1][0]:l[i][1]])
        
    print(max1)
        

def main():
    N = int(rl())
    A = list(map(int,rl().split()))

    compute(A,N)
    
main()