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 A {

    public static void main(String[] args) {
        FastReader scan = new FastReader();
        PrintWriter out = new PrintWriter(System.out);
        Task solver = new Task();
        int t = 1;
        while (t --> 0) solver.solve(1, scan, out);
        out.close();
    }

    static class Task {
        public void solve(int testNumber, FastReader scan, PrintWriter out) {
            int n = scan.nextInt();
            int[] a = new int[n];
            ArrayList<Range> ranges = new ArrayList<>();
            int currBegin = 0;
            for(int i = 0; i < n; i++) {
                a[i] = scan.nextInt();
                if(i > 0 && a[i] <= a[i-1]) {
                    ranges.add(new Range(currBegin, i-1));
                    currBegin = i;
                }
            }
            ranges.add(new Range(currBegin, n-1));
            int max = calc(ranges.get(0));
            for(int i = 1; i < ranges.size(); i++) {
                max = Math.max(max, calc(ranges.get(i)));
                max = Math.max(max, check(ranges.get(i-1), ranges.get(i), a));
            }
            out.println(max);
        }
        
        static int calc(Range a) {
            return a.end - a.start+1;
        }
        
        static int check(Range a, Range b, int[] c) {
            int left = Math.max(a.start, a.end-1);
            int right = Math.min(b.end, b.start+1);
            return c[left] < c[b.start] || c[right] > c[a.end] ? b.end - a.start : 0;
        }
        
        static class Range {
            int start, end;
            
            public Range(int a, int b) {
                start = a;
                end = b;
            }
        }
    }

    static void shuffle(int[] a) {
        Random get = new Random();
        for (int i = 0; i < a.length; i++) {
            int r = get.nextInt(a.length);
            int temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }

    static void shuffle(long[] a) {
        Random get = new Random();
        for (int i = 0; i < a.length; i++) {
            int r = get.nextInt(a.length);
            long temp = a[i];
            a[i] = a[r];
            a[r] = temp;
        }
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public FastReader(String s) throws FileNotFoundException {
            br = new BufferedReader(new FileReader(new File(s)));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}