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.math.BigInteger;
import java.util.*;


public class Main {

    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(1, in, out);
        out.close();
    }

    static class Task {

        public void solve(int testNumber, InputReader input, PrintWriter out) {
//            int t = input.nextInt();

//            while (t-- > 0){
                int n = input.nextInt();

                List<Node> list = new ArrayList<>();

                list.add(new Node(0,0,new ArrayList<>()));
                int pre = -1;
                boolean flag = true;
                for(int i = 0;i < n;i++){
                    int x = input.nextInt();

                    if(i == 0){
                        list.get(0).list.add(x);
                        pre = x;
                    }
                    else{
                        if(x > pre){
                            list.get(list.size() - 1).list.add(x);
                            flag = true;
                        }
                        else{
                            list.get(list.size() - 1).end = i;
                            list.add(new Node(i,0,new ArrayList<>()));
                            list.get(list.size() - 1).list.add(x);
                            flag = false;
                        }
                        pre = x;
                    }
                }

//                out.println(list);

                if(list.size() == 1){
                    System.out.println(list.get(0).list.size());
                }
                else{
                    int ans = -20000005;
                    for(Node node:list){
                        ans = Math.max(ans,node.list.size());
                    }

                    for(int i = 1;i < list.size();i++){
                        List<Integer> now = list.get(i).list;
                        List<Integer> pre1 = list.get(i - 1).list;

                        if(now.size() != 1 || i == list.size() - 1){
                            int nowNum = get(now,1);

                            if(nowNum > pre1.get(pre1.size() - 1)){
                                ans = Math.max(ans,now.size() - 1 + pre1.size());
                            }
                            int preNum = get(pre1,0);
                            if(preNum < now.get(0)){
                                ans = Math.max(ans,pre1.size() - 1 + now.size());
                            }

                        }
                        else{
                            List<Integer> after = list.get(i + 1).list;

                            int t1 = pre1.get(pre1.size() - 1);
                            int t2 = after.get(0);

                            if(t1 < t2){
                                ans = Math.max(ans,pre1.size() + after.size());
                            }
                        }
                    }
                    out.println(ans);
                }

                out.flush();

//            }




        }

        public int get(List<Integer> list,int op){
            if(op == 0){
                if(list.size() == 1){
                    return -1;
                }

                return list.get(list.size() - 2);
            }
            else{
                if(list.size() == 1){
                    return 200005;
                }

                return list.get(1);
            }
        }

        public class Node{
            int start,end;
            List<Integer> list;

            Node(int start,int end,List<Integer> list){
                this.list = list;
                this.end = end;
                this.start = start;
            }

            @Override
            public String toString() {
                return "Node{" +
                        "start=" + start +
                        ", end=" + end +
                        ", list=" + list +
                        '}';
            }
        }


    }

    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());
        }

        public float nextFloat() {
            return Float.parseFloat(next());
        }

        public BigInteger nextBigInteger(){
            return new BigInteger(next());
        }


    }
}