DZY has a sequence a, consisting of n integers.

We'll call a sequence ai, ai + 1, ..., aj (1 ≤ i ≤ j ≤ n) a subsegment of the sequence a. The value (j - i + 1) denotes the length of the subsegment.

Your task is to find the longest subsegment of a, such that it is possible to change at most one number (change one number to any integer you want) from the subsegment to make the subsegment strictly increasing.

You only need to output the length of the subsegment you find.

Input

The first line contains integer n (1 ≤ n ≤ 105). The next line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109).

Output

In a single line print the answer to the problem — the maximum length of the required subsegment.

Examples

Input

6
7 2 3 1 5 6


Output

5

Note

You can choose subsegment a2, a3, a4, a5, a6 and change its 3rd element (that is a4) to 4.
import java.io.*;
import java.util.*;
import java.text.DecimalFormat;
public class Main {

    private static BufferedReader br;
    private static PrintWriter ou;
    private static StringBuilder sb;

    public static void solve() throws Exception {
        int  n = readInt(br);

        int[] arr = readIntArray(br);

        int[] len = new int[n];

        len[n - 1] = 1;

        for (int i = n - 2; i >= 0; i --) {
            len[i] = 1;
            if (arr[i + 1] > arr[i])
                len[i] += len[i + 1];
        }
        int[] rlen = new int[n];
        rlen[0] = 1;
        for (int i = 1; i < n; i ++) {
            rlen[i] = 1;
            if (arr[i] > arr[i - 1])
                rlen[i] += rlen[i - 1];
        }
        int ans = 1;

        // Check on replacing last
        int x = arr[n - 1];
        arr[n - 1] = Integer.MAX_VALUE;
        for (int i = n - 2; i >= 0; i --) {
            if (arr[i] >= arr[i + 1])
                break;
            ans ++;
        }
        arr[n - 1] = x;

        int curr = 1;
        // Check on replacing first
        x = arr[0];
        arr[0] = Integer.MIN_VALUE;
        for (int i = 1; i < n; i ++) {
            if (arr[i] <= arr[i - 1])
                break;
            curr ++;
        }
        arr[0] = x;
        ans = Math.max(ans, curr);


        /*for (int i : len)
            System.out.print(i  + " ");
        System.out.println();*/

        for (int i = 1; i < n - 1; i ++) {
            boolean check = (arr[i + 1] - arr[i - 1] > 1);
            ans = Math.max(ans, 1 + len[i + 1]);
            ans = Math.max(ans, 1 + rlen[i - 1]);
            ans = Math.max(ans, len[i]);
            ans = Math.max(ans, rlen[i]);

            if (check) {
                ans = Math.max(ans, len[i + 1] + rlen[i - 1] + 1);
            }
        }

        sb.append(ans);
    }


    
    public static void main(String[] args) throws Exception {
        br = new BufferedReader(new InputStreamReader(System.in));
        ou = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        sb = new StringBuilder("");

        int t = 1; // readInt(br);

        while (t-- > 0) {
            solve();
        }

        ou.print(sb.toString());
        ou.close();
        br.close();

        System.exit(0);
    }

    public static int readInt(BufferedReader br) throws IOException {
        return Integer.parseInt(br.readLine());
    }

    public static double readDouble(BufferedReader br) throws IOException {
        return Double.parseDouble(br.readLine());
    }

    public static String readString(BufferedReader br) throws IOException {
        return br.readLine();
    }

    public static int[] readIntArray(BufferedReader br) throws IOException {
        String[] pts = br.readLine().split(" ");
        int[] arr = new int[pts.length];
        for (int i = 0 ; i < pts.length; i ++) {
            arr[i] = Integer.parseInt(pts[i]);
        }
        return arr;
    }

    public static double[] readDoubleArray(BufferedReader br) throws IOException {
        String[] pts = br.readLine().split(" ");
        double[] arr = new double[pts.length];
        for (int i = 0 ; i < pts.length; i ++) {
            arr[i] = Double.parseDouble(pts[i]);
        }
        return arr;
    }

    public static int toInt(String s) {
        return Integer.parseInt(s);
    }
    
    public static double toDouble(String s) {
        return Double.parseDouble(s);
    }

}
