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 java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.List;
import java.util.Scanner;

public class CF {

	private static Scanner cin = new Scanner(System.in);
	static final int N = 100111;
	static int tc;
	int n;
	int a[], dp[][];
	int b[], c[];
	public void input() {
		n = cin.nextInt();
		a = new int[n];
		b = new int[n];
		c = new int[n];
		dp = new int[n][2];
		int ans = 1;
		for (int i = 0; i < n; i++) {
			a[i] = cin.nextInt();
			if (i == 0) {
				b[i] = 1;
			} else if (a[i] > a[i-1]) {
				b[i] = b[i-1] + 1;
			} else {
				b[i] = 1;
			}
			if (ans < b[i]) {
				ans = b[i];
			}
		}
		
		int k = 1;
		for (int i = n - 2; i > 0; i--) {
			if (a[i-1] < a[i+1] && k + b[i-1] > ans) {
				ans = k + b[i-1];
			}
			if (a[i] < a[i+1]) {
				k++;
			} else {
				k = 1;
			}
			if (ans < k) {
				ans = k;
			}
			if (a[i] > a[i-1]) {
				if (k + b[i-1] > ans) {
					ans = k + b[i-1];
				}
			}
		}
		
		System.out.println(ans);
	}
	
	public void solve() {
		
	}
	public static void main(String[] args) {
		
		CF cf = new CF();
		
		while (cin.hasNext()) {
			cf.input();
			cf.solve();
		}
	}
}
