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 D {
    Random random = new Random(751454315315L + System.currentTimeMillis());

    public void solve() throws IOException {
        int n = nextInt();
        int[] a = new int[n + 1];
        for (int i = 0; i < n; i++) {
            a[i] = nextInt();
        }
        a[n] = -1;
        int[] dp = new int[n + 2];
        int[] dp1 = new int[n + 2];
        dp[n + 1] = 0;
        dp[0] = 1;
        dp1[0] = 1;
        for (int i = 1; i < n + 1; i++) {
            if (a[i] > a[i - 1]) {
                dp[i] = dp[i - 1] + 1;
                dp1[i] = dp1[i - 1] + 1;
            } else {
                dp[i] = 1;
                dp1[i] = 1;
                int x = dp[i - 1] + 1;
                int q = i - 1;
                for (int j = x - 1; j > 0; j--) {
                    dp[q] = x - dp[q];
                    q--;
                }
            }
        }
        int max = dp[0];
        dp1[n] = 0;
        for (int i = 1; i < n; i++) {
            if (a[i - 1] < a[i + 1]) {
                max = Math.max(max, dp[i + 1] + dp1[i - 1]);
            }
            max = Math.max(max, dp1[i]);
        }
        out.print(max);
    }

    public void run() {
        try {
            br = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);

            solve();

            out.close();
        } catch (IOException e) {
            e.printStackTrace();
            System.exit(1);
        }
    }

    private void shuffle(int[] s) {
        for (int i = 0; i < s.length; ++i) {
            int j = random.nextInt(i + 1);
            int t = s[i];
            s[i] = s[j];
            s[j] = t;
        }
    }

    class Pair implements Comparable<Pair> {
        int f;
        int s;

        public Pair(int f, int s) {
            this.f = f;
            this.s = s;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Pair pair = (Pair) o;
            return f == pair.f &&
                    s == pair.s;
        }

        @Override
        public int hashCode() {
            return Objects.hash(f, s);
        }

        @Override
        public int compareTo(Pair o) {
            if (f == o.f) {
                return s - o.s;
            }
            return f - o.f;
        }
    }

    BufferedReader br;
    StringTokenizer in;
    PrintWriter out;

    public String nextToken() throws IOException {
        while (in == null || !in.hasMoreTokens()) {
            in = new StringTokenizer(br.readLine());
        }
        return in.nextToken();
    }

    public int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    public double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    public long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    public int[] nextArr(int n) throws IOException {
        int[] res = new int[n];
        for (int i = 0; i < n; i++) {
            res[i] = nextInt();
        }
        return res;
    }

    public static void main(String[] args) throws IOException {
        Locale.setDefault(Locale.US);
        new D().run();
    }
}