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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

import static java.lang.Math.log;
import static java.lang.Math.min;

public class First {

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskA solver = new TaskA();
        int t;
        //t = in.nextInt();
        t = 1;
        while (t > 0) {
            solver.call(in,out);
            t--;
        }
        out.close();

    }

    static class TaskA {
        public void call(InputReader in, PrintWriter out) {
            int n , a=1, b=0, max = Integer.MIN_VALUE;
            n = in.nextInt();

            int[] arr = new int[n];

            for (int i = 0; i < n; i++) {
                arr[i] = in.nextInt();
            }

            for (int i = 0 , j=0; i < n-1; i++) {

                if(arr[i]<arr[i+1]){
                    a++;
                }
                else if(arr[i]==arr[i+1]){
                    if(b==0)
                        b++;
                    else{
                        max = Math.max(a,max);
                        a = 1;
                        b = 0;
                    }
                }
                else{
                    if(i!=n-2){
                        if(b==0) {
                            if(arr[i]<arr[i+2] && arr[i+1]<arr[i+2]){
                                j = i;
                            }
                            if(a==1) {
                                if (arr[i] < arr[i + 2]) {
                                    j = i;
                                    i++;
                                    a++;
                                    b++;

                                }
                                else if(arr[i+1]>=arr[i+2] || arr[i]>=arr[i+2]){
                                    max = Math.max(a, max);
                                    a = 1;
                                    if (j != 0) {
                                        i = j;
                                        j = 0;
                                    }
                                }
                            }
                            else{
                                if (arr[i] < arr[i + 2]) {
                                    j = i;
                                    i++;
                                    a++;
                                    b++;

                                }
                                else if (arr[i + 1] < arr[i + 2] && arr[i-1] <arr[i+1]) {
                                    b++;
                                }
                                else {
                                    max = Math.max(a, max);
                                    a = 1;
                                    if (j != 0) {
                                        i = j;
                                        j = 0;
                                    }
                                }
                            }
                        }
                        else{
                            max = Math.max(a,max);
                            a = 1;
                            b = 0;
                            if(j!=0){
                                i = j;
                                j = 0;
                            }
                        }
                    }
                    else{
                        max =Math.max(a, max);
                        a = 1;
                        b = 0;
                        if(j!=0){
                            i = j;
                            j = 0;
                        }
                    }
                }

            }
            max = Math.max(max , a);
            out.println(max);

        }
    }

    static class answer implements Comparable<answer> {
        int a, b;

        public answer(int a, int b) {
            this.a = a;
            this.b = b;
        }

        @Override
        public int compareTo(answer o) {
            return o.a - this.a;
        }
    }

    static long gcd(long a, long b)
    {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }

    static void sort(int[] a) {
        ArrayList<Integer> l=new ArrayList<>();
        for (int i:a) l.add(i);
        Collections.sort(l);
        for (int i=0; i<a.length; i++) a[i]=l.get(i);
    }

    static final Random random=new Random();

    static void shuffleSort(int[] arr) {
        int n=arr.length;
        for (int i=0; i<n; i++) {
            int a=random.nextInt(n), temp=arr[a];
            arr[a]=arr[i];
            arr[i]=temp;
        }
        Arrays.sort(arr);
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong(){
            return Long.parseLong(next());
        }
        public double nextDouble() {
            return Double.parseDouble(next());
        }

    }
}