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.IOException;
import java.io.InputStream;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.List;

import javax.xml.stream.events.EndDocument;

/**
 * @author duy
 * 
 */
public class A4 {
	public static void main(String[] args) {
		input();
		for (int i = 0; i < nTestCases; i++) {
			solve(i);
		}

	}

	static void solve(int k) {
		int[] s = a[k];
		int length = n[k];
		StringBuilder res = new StringBuilder();

		if (length == 1) {
			System.out.println(1);
			return;
		}

		int end = 0;
		int start = 0;
		int preEnd = -1;
		int nextstart = -1;
		int count = 0;
		int sum = 0;
		int sumLeft = 0;
		int max = 0;
		boolean check = false;

		for (int i = 0; i < length - 1; i++) {
			if (i == length - 2 && s[i] < s[i + 1]) {
				count++;
			}
			count++;
			if (s[i] >= s[i + 1] || (i == length - 2 && s[i] < s[i + 1])) {
				sum = count;
				end = s[i];
				start = s[i + 1];
				preEnd = i - 1 >= 0 ? s[i - 1] : start;
				nextstart = i + 2 <= length - 1 ? s[i + 2] : end;
				if (check) {
					max = Math.max(sum + sumLeft, max);
					check = false;
				}
				if (start - preEnd > 1 || nextstart - end > 1) {
					check = true;
					sumLeft = sum;
				}
				max = Math.max(sum, max);
				if (sum + 1 <= length) {
					sum +=1;
				}
				max = Math.max(sum, max);
				count = 0;
			}
		}
		System.out.println(max);
	}

	/*********************************** INPUT *********************************************/

	static int nTestCases; // number of testcases
	static int[] n; // length of ith testcase
	static int[][] a; // ith arrays

	static void input() {
		// nTestCases = nextInt();
		nTestCases = 1;
		n = new int[nTestCases];
		a = new int[nTestCases][];
		for (int i = 0; i < nTestCases; i++) {
			n[i] = nextInt();
			a[i] = nextAi(n[i]);
		}
	}

	/******************************** BASIC READER ***************************************/
	static InputStream is = System.in;
	static private byte[] buffer = new byte[1024];
	static private int lenbuf = 0, ptrbuf = 0;

	static private int readByte() {
		if (lenbuf == -1)
			throw new InputMismatchException();
		if (ptrbuf >= lenbuf) {
			ptrbuf = 0;
			try {
				lenbuf = is.read(buffer);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (lenbuf <= 0)
				return -1;
		}
		return buffer[ptrbuf++];
	}

	static private boolean isSpace(int c) {
		return !(c >= 33 && c <= 126);
	}

	static private int read() {
		int b;
		while ((b = readByte()) != -1 && isSpace(b))
			;
		return b;
	}

	static private double nextDouble() {
		return Double.parseDouble(nextString());
	}

	static private char nextChar() {
		return (char) read();
	}

	static private String nextString() {
		int b = read();
		StringBuilder sb = new StringBuilder();
		while (!(isSpace(b))) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	static private char[] nextString(int n) {
		char[] buf = new char[n];
		int b = read(), p = 0;
		while (p < n && !(isSpace(b))) {
			buf[p++] = (char) b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}

	static private int nextInt() {
		int num = 0, b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}

		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	private long nextLong() {
		long num = 0;
		int b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}

		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	static private int[] nextAi(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = nextInt();
		return a;
	}
}