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.
# -*- coding: utf-8 -*-

n = int(input().strip())
a = [int(j) for j in input().strip().split()]
a.append(0)


b = [a[0]]
r = []
for i in range(len(a)-1):
    left = a[i]
    right = a[i+1]
    if right > left:
        b.append(right)
    else:
        r.append(b)
        b = [a[i+1]]
        

def find_len(list1,list2,list3):
    max_len = max(len(list1), len(list2), len(list3))
    
    if len(list2) == 1:
        if list1[-1] < list3[0]:
            max_len = len(list1) + len(list3)
    else:
        if list2[1] > list1[-1]:
            m_len = len(list1) + len(list2) - 1
            if m_len > max_len:
                max_len = m_len 
                
        if len(list1) >=2:
            if list1[-2] < list2[0]:
                m_len = len(list1) + len(list2) - 1
                if m_len > max_len:
                    max_len = m_len 
            
        if list2[-2] < list3[0]:
            m_len = len(list3) + len(list2) - 1
            if m_len > max_len:
                max_len = m_len
                
                      
        if len(list3) >=2:
            if list3[1] > list2[-1]:
                m_len = len(list3) + len(list2) - 1
                if m_len > max_len:
                    max_len = m_len 
                
    return max_len
    
res = 0

if len(r) < 3:
    r.extend([[0],[0]])
 
for mi in range(len(r) - 2):
    l1 = r[mi]
    l2 = r[mi+1]
    l3 = r[mi+2]
    
    mr = find_len(l1,l2,l3)
    if mr > res:
        res = mr
        
print(res)