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.*;

public class tank {

    static final FastScanner fs = new FastScanner();

    public static void main(String[] args) {
//        int t = fs.nextInt();
//        while(t-->0) {
//            run_case();
//        }

        run_case();
    }

    static void run_case() {
        int n = fs.nextInt(), netmax = 0, cur = 0;
        int[] arr = fs.readArray(n);

        int[] left = new int[n];
        int[] right = new int[n];

        Arrays.fill(left, 1);
        Arrays.fill(right, 1);

        for (int i = n - 1; i > 0 ; i--) {
            if(arr[i] > arr[i - 1]){
                cur++;
                right[i] = cur;
                netmax = Math.max(netmax, right[i]);
            }else{
                right[i] = cur + 1;
                netmax = Math.max(netmax, right[i]);
                cur = 0;
            }

            if(i == 1){
                right[0] = cur + 1;
                netmax = Math.max(netmax, right[0]);
            }
        }

        cur =0;

        for (int i = 0; i < n - 1; i++) {
            if(arr[i + 1] >  arr[i]){
                cur++;
                left[i] = cur;
            }else {
                left[i] = cur + 1;
                cur = 0;
            }

            if(i == n - 2){
                left[n - 1] = cur + 1;
            }
        }

        for (int i = 1; i < n - 1; i++) {
            if(arr[i - 1] < arr[i + 1]){
                netmax = Math.max(netmax, left[i - 1] + right[i + 1]);
            }
        }

        System.out.println(netmax);
    }

    static class FastScanner {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        String next() {
            while (!st.hasMoreTokens())
                try {
                    st=new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        int[] readArray(int n) {
            int[] a=new int[n];
            for (int i=0; i<n; i++) a[i]=nextInt();
            return a;
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }
    }
}