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.util.*;
import java.io.*;
import static java.lang.Math.*;
import java.math.BigInteger;

public class D {

    public static void main(String[] args) throws Exception {
        FastScanner scanner = new FastScanner();

        int n = scanner.nextInt();
        long[] a = scanner.nextLongArray();

        ArrayList<Pair> p = new ArrayList <>();
        int l = 0;
        int mx = Integer.MIN_VALUE;
        for (int i = 1; i < n; i++) {
            if (a[i] <= a[i - 1]) {
                p.add(new Pair(l, i - 1));
                //System.out.println(mx);
                mx = max(mx, i - l);
                l = i;
                //System.out.println(mx);
            }
        }
        p.add(new Pair(l, n - 1));
        mx = max(mx, p.get(p.size() - 1).y - p.get(p.size() -1).x + 1);
        for (int i = 1; i < p.size(); i++) {
            if (p.get(i - 1).y == p.get(i).x - 1) {
                Pair p1 = p.get(i - 1);
                Pair p2 = p.get(i);
                if ((p2.x + 1 < n && a[p1.y] < a[p2.x + 1]) || (p1.y > 0 && a[p1.y - 1] < a[p2.x]))
                    mx = max(mx, p1.y - p1.x + p2.y - p2.x + 1);
            }
        }
        System.out.println(mx);
    }

    public static class Pair {
        int x, y;
        public Pair(int x, int y) {
            this.x = x;
            this.y = y;
        }

    }

    private static class FastScanner {
        private BufferedReader br;

        public FastScanner() { br = new BufferedReader(new InputStreamReader(System.in)); }
        public FastScanner(String input) throws Exception { br = new BufferedReader(new FileReader(input)); }
        public int[] nextIntArray() throws IOException {
            String line = br.readLine();
            String[] strings = line.trim().split("\\s+");
            int[] array = new int[strings.length];
            for (int i = 0; i < array.length; i++)
                array[i] = Integer.parseInt(strings[i]);
            return array;
        }
        public int nextInt() throws IOException { return Integer.parseInt(br.readLine()); }
        public long[] nextLongArray() throws IOException {
            String line = br.readLine();
            String[] strings = line.trim().split("\\s+");
            long[] array = new long[strings.length];
            for (int i = 0; i < array.length; i++)
                array[i] = Long.parseLong(strings[i]);
            return array;
        }
        public ArrayList<Integer> nextIntegerArrayList() throws IOException {
            String line = br.readLine();
            String[] strings = line.trim().split("\\s+");
            ArrayList<Integer> array = new ArrayList<Integer>();
            for (int i = 0; i < strings.length; i++)
                array.add(Integer.parseInt(strings[i]));
            return array;
        }
        public ArrayList<Long> nextLongArrayList() throws IOException {
            String line = br.readLine();
            String[] strings = line.trim().split("\\s+");
            ArrayList<Long> array = new ArrayList<Long>();
            for (int i = 0; i < strings.length; i++)
                array.add(Long.parseLong(strings[i]));
            return array;
        }
        public long nextLong() throws IOException { return Long.parseLong(br.readLine()); }
        public double nextDouble() throws IOException { return Double.parseDouble(br.readLine()); }
        public String nextLine() throws IOException { return br.readLine(); }


        public ArrayList<BigInteger> nextBigIntegers() throws IOException {
            String line = br.readLine();
            String[] strings = line.trim().split("\\s+");
            ArrayList<BigInteger> array = new ArrayList<BigInteger>();
            for (int i = 0; i < strings.length; i++)
                array.add(BigInteger.valueOf(Long.valueOf(strings[i])));
            return array;
        }
    }
}
