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.
#include <bits/stdc++.h>
using namespace std;
int n;
int arr[200005];
int main() {
  cin >> n;
  for (int i = 0; i < n; i++) cin >> arr[i];
  int shamne[n], pos = 0;
  int pisone[n];
  shamne[0] = 1;
  int cnt = 1;
  for (int i = 1; i < n; i++) {
    if (arr[i] > arr[i - 1])
      shamne[i] = shamne[i - 1] + 1;
    else {
      shamne[i] = 1;
      for (int j = i - 1; j >= pos; j--) pisone[j] = cnt++;
      pos = i;
      cnt = 1;
    }
  }
  for (int j = n - 1; j >= pos; j--) pisone[j] = cnt++;
  int ans = 1;
  if (arr[1] > arr[0]) ans = 2;
  for (int i = 2; i < n; i++) {
    if (arr[i] <= arr[i - 1] && arr[i] > arr[i - 2]) {
      ans = max(shamne[i - 2] + pisone[i], ans);
    }
    if (i < n - 1 && arr[i] <= arr[i - 1] && arr[i + 1] > arr[i - 1]) {
      ans = max(shamne[i - 1] + pisone[i + 1], ans);
    }
    ans = max(shamne[i], ans);
  }
  cout << ans << endl;
}
