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.
//package exercise2;

import java.io.DataInputStream;
import java.io.IOException;

public class q5 {
    static int[] a;
    static int max_length_change, max_length;
    public static void main(String[] args) {
        try {
            Reader reader = new Reader();
            int n = reader.nextInt();
            a = new int[n];
            for(int i = 0 ; i < n; i++){
                a[i] = reader.nextInt();
            }
            max_length=1;
            max_length_change=1;
            int[] ascending_lengths = new int[n];
            int[] ascending_last = new int[n];
            ascending_lengths[0] = 1;
            for(int i = 1 ; i < n; i++){
                if(a[i] > a[i-1]){
//                    System.out.println("in if");
                    ascending_lengths[i] = ascending_lengths[i-1]+1;
                }else{
                    ascending_lengths[i] = 1;
                }
            }
//            System.out.println("ascending from top : ");
//            for (int ascending_length : ascending_lengths) {
//                System.out.print(ascending_length + " ");
//            }
//            System.out.println();

            ascending_last[n-1] = 1;
            for(int i = n-2; i >= 0 ; i--){
                if(a[i] < a[i+1]){
                    ascending_last[i] = ascending_last[i+1]+1;
                }else{
                    ascending_last[i] = 1;
                }

            }
//            System.out.println("ascending bottom: ");
//            for (int j : ascending_last) {
//                System.out.print(j + " ");
//            }
//            System.out.println();

            int result = 1;
            int current = 1;
            for(int i = 1; i < n; i++){
                if(i < n-1) {
                    if (a[i - 1] < a[i + 1]) {
                        current = ascending_lengths[i - 1] + ascending_last[i + 1];
                        if(current > result){
                            result = current;
                        }
//                        result = Math.max(result, ascending_lengths[i - 1] + ascending_last[i + 1]);
                    }
                }
                result = Math.max(result, ascending_lengths[i]);
            }

            System.out.println(result);
        }catch (Exception e){
            e.printStackTrace();
        }

    }

    static class Reader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public Reader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }
        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }
    }
}
