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 solve():
    n = int(input())
    nums = [int(x) for x in input().split()]

    dp = [[1]*n for i in range(2)]
    # print(dp)
    flag = [0]*n
    if n==0:
        print(0)
        return
    if n==1:
        print(1)
        return
    if n==2:
        if nums[0]<nums[1]:
            print(2)
        else:
            print(1)
        return
    dp[0][0]=1
    dp[0][1]=0

    if nums[0]<nums[1]:
        dp[0][1]=2
    else:
        dp[0][1]=1
    dp[1][1]=1


    for i in range(2,n):
        if nums[i]>nums[i-1]:
            dp[0][i]=dp[0][i-1]+1
            dp[1][i]=dp[1][i-1]+1



        if nums[i]>nums[i-2]:
                # print(5)
                dp[1][i]=max(dp[1][i],dp[0][i-2]+1)

            # dp[1][i]=max(dp[i],dp[i-2]+1)
        # dp[i]=max(dp[i],1)
    # print(dp)
    ans = 0
    for i in range(2):
        for j in range(n):
            ans = max(ans,dp[i][j])
    # print(dp)
    print(ans)
solve()
