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.*;
public class DZY_KADANE
{
    public static void main(String[]args)
    {
        InputReader1 sc = new InputReader1(System.in);
        int N = sc.nextInt();
        int A[] = new int [N+2] , L[] = new int [N+2] , R[] = new int [N+2];
        for(int i=1;i<=N;i++)
        A[i] = sc.nextInt();
        /*424238336 649760493 681692778 714636916 719885387 804289384 846930887 957747794 596516650 189641422
           1         2         3        4          5         6        7        8          1         1
           8         7         6        5          4         3        2        1          1         1*/
        L[N+1]=R[N+1]=0;   
        L[0] = R[0] = 0;
        int best = 0;
        for(int i=1;i<=N;i++)
        {
            L[i] = 1;
            if(A[i] > A[i-1])
                L[i] = L[i-1]+1;
            best = Math.max(best,L[i]);    
        }
        for(int i=N;i>=1;i--)
        {
            R[i] = 1;
            if(A[i] < A[i+1] && i!=N)
                R[i] = R[i+1]+1;
            best = Math.max(best,R[i]);    
        }
        for(int i=2;i<N;i++)
            if(A[i-1]+1<A[i+1])best = Math.max(best,R[i+1]+L[i-1]+1);
        for(int i=1;i<N;i++)
            best=Math.max(L[i]+1,best);
        for(int i=N; i>1 ; i--)
            best=Math.max(best,R[i]+1);
        System.out.println(best);    
    }
}
class InputReader1 
{

    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;

    public InputReader1(InputStream stream) {
        this.stream = stream;
    }

    public int read() {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }

    public int nextInt() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c & 15;
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public long nextLong() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        long res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c & 15;
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

    public String next() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));
        return res.toString();
    }

    public String nextLine() {
        int c = read();
        //while (c != '\n' && c != '\r' && c != '\t' && c != -1)
        //c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (c != '\n' && c != '\r' && c != '\t' && c != -1);
        return res.toString();
    }

    public static boolean isSpaceChar(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }

}   