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.
def seq_len(arr, n):
    seqs=[]
    seq_b =0
    seq_e =0
    longest = -1
    for i in range(0, n - 1) :
        if arr[i + 1] > arr[i]:
            seq_e = i + 1
        else:
            longest = max(longest, seq_e - seq_b + 1)
            seqs.append((seq_b, seq_e))
            seq_b = i + 1 
            seq_e = i + 1
    longest = max(longest, seq_e - seq_b + 1)       
    seqs.append((seq_b, seq_e))
    #print(seqs) 
    if len(seqs) > 1:         
        for i in range(0, len(seqs)-1):
            if seqs[i][1] - 1 >= 0:
                if arr[seqs[i][1] - 1] < arr[seqs[i+1][0]]:
                    longest = max(longest, seqs[i][1] - seqs[i][0] + 1 +  seqs[i+1][1] - seqs[i+1][0])
                                                         
            if seqs[i+1][0]+1 < n:
                if arr[seqs[i][1]] < arr[seqs[i+1][0] + 1]:                    
                    longest = max(longest, seqs[i][1] - seqs[i][0] + 1 +  seqs[i+1][1] - seqs[i+1][0])                    
        return longest
    else:
        return n
     

n = int(input())
arr=[int(x) for x in input().split()]
print(seq_len(arr, n))
