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.io.*;
import java.util.*;
import java.math.*;

public class p1272D {

	public int n;
	public int[] a;
	public int[][][][] memo;
	public int[][][][] memo2;

	public int dp(int ind, int usedremove, int dominustwo, int isstart) {
		if(ind >= n) {
			return 0;
		}

		if(memo[ind][usedremove][dominustwo][isstart] != -1) {
			return memo[ind][usedremove][dominustwo][isstart];
		}

		if(isstart == 1) {
			memo[ind][usedremove][dominustwo][isstart] = 1 + dp(ind + 1, 0, 0, 0);
			return memo[ind][usedremove][dominustwo][isstart] ;
		}

		int offset = 1;

		if(dominustwo == 1) {
			offset = 2;
		}

		if(ind - offset < 0) {
			memo[ind][usedremove][dominustwo][isstart]  = 0 + dp(ind + 1, usedremove, 0, 0);
			return memo[ind][usedremove][dominustwo][isstart];
		}

		if(a[ind] <= a[ind - offset]) {
			if(usedremove == 1) {
				memo[ind][usedremove][dominustwo][isstart] = 0;
				return memo[ind][usedremove][dominustwo][isstart] ;
			}

			memo[ind][usedremove][dominustwo][isstart]  = 0 + dp(ind, 1, 1, 0);
			return memo[ind][usedremove][dominustwo][isstart] ;
		}

		memo[ind][usedremove][dominustwo][isstart]  = 1 + dp(ind + 1, usedremove, 0, 0);

		if(dominustwo == 1) {
			memo[ind][usedremove][dominustwo][isstart]--;
			
		} 
		return memo[ind][usedremove][dominustwo][isstart] ;


	}

	public int dp2(int ind, int usedremove, int dominustwo, int isstart) {
		if(ind >= n) {
			return 0;
		}

		if(memo2[ind][usedremove][dominustwo][isstart] != -1) {
			return memo2[ind][usedremove][dominustwo][isstart];
		}

		if(isstart == 1) {
			memo2[ind][usedremove][dominustwo][isstart] = 1 + dp2(ind + 1, 0, 0, 0);
			return memo2[ind][usedremove][dominustwo][isstart] ;
		}

		int offset = 1;

		if(dominustwo == 1) {
			offset = 2;
		}

		if(ind - offset < 0) {
			memo2[ind][usedremove][dominustwo][isstart]  = 0 + dp2(ind + 1, usedremove, 0, 0);
			return memo2[ind][usedremove][dominustwo][isstart];
		}

		if(a[ind] <= a[ind - offset]) {
			if(usedremove == 1) {
				memo2[ind][usedremove][dominustwo][isstart] = 0;
				return memo2[ind][usedremove][dominustwo][isstart] ;
			}

			memo2[ind][usedremove][dominustwo][isstart]  = 0 + dp2(ind + 1, 1, 1, 0);
			return memo2[ind][usedremove][dominustwo][isstart] ;
		}

		memo2[ind][usedremove][dominustwo][isstart]  = 1 + dp2(ind + 1, usedremove, 0, 0);

		if(dominustwo == 1) {
			//memo[ind][usedremove][dominustwo][isstart]--;
			
		} 
		return memo2[ind][usedremove][dominustwo][isstart] ;


	}

	public void realMain() throws Exception {

		BufferedReader fin = new BufferedReader(new InputStreamReader(System.in), 1000000);

		String in = fin.readLine();

		String[] ar = in.split(" ");

		n = Integer.parseInt(ar[0]);
		
		a = new int[n];

		for(int i = 0; i < n; i++) {
			int ret = 0;
			boolean dig = false;
			for (int ch = 0; (ch = fin.read()) != -1; ) {
        			if (ch >= '0' && ch <= '9') {
            				dig = true;
           				ret = ret * 10 + ch - '0';
        			} else if (dig) break;
    			}

			a[i] = ret;
		}

		memo = new int[n][2][2][2];
		memo2 = new int[n][2][2][2];

		for(int i = 0; i < n; i++) {
			memo[i][0][0][0] = -1;
			memo[i][0][0][1] = -1;
			memo[i][0][1][0] = -1;
			memo[i][0][1][1] = -1;
			memo[i][1][0][0] = -1;
			memo[i][1][0][1] = -1;
			memo[i][1][1][0] = -1;
			memo[i][1][1][1] = -1;

			memo2[i][0][0][0] = -1;
			memo2[i][0][0][1] = -1;
			memo2[i][0][1][0] = -1;
			memo2[i][0][1][1] = -1;
			memo2[i][1][0][0] = -1;
			memo2[i][1][0][1] = -1;
			memo2[i][1][1][0] = -1;
			memo2[i][1][1][1] = -1;
		}

		int max = 0;

		for(int i = 0; i < n; i++) {
			max = Math.max(max, dp(i, 0, 0, 1));
			//System.out.println("memo: " + memo[i][0][0][1]);
		}

		for(int i = 0; i < n; i++) {
			max = Math.max(max, dp2(i, 0, 0, 1));
			//System.out.println("memo2: " + memo2[i][0][0][1]);
		}

		System.out.println(max);



	}


	public static void main(String[] args) throws Exception {
		p1272D a = new p1272D();
		a.realMain();
	}
}