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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

import static java.lang.Math.max;


public class Main {
    public static void main(String[] args) throws IOException {
        FastScanner scanner = new FastScanner();
        int n = scanner.nextInt();
        int[] ns = new int[n];
        for (int i = 0; i < n; i++) {
            ns[i] = scanner.nextInt();
        }

        System.out.println(countMaxSeqL(ns));
    }

    private static int countMaxSeqL(int[] a) {
        int globalSMax = 1;
        int curMax = 1;
        int prevCurMax = 0;
        int gapPointR = -1;
        int gapPointL = -1;
        for (int i = 1; i < a.length; i++) {
            if (a[i] > a[i - 1]) {
                curMax++;
                continue;
            }
            globalSMax = max(globalSMax, curMax);
            if (gapPointR != -1) {
                globalSMax = max(globalSMax, prevCurMax + curMax - 1);
            }
            if (gapPointL != -1) {
                globalSMax = max(globalSMax, prevCurMax + curMax - 1);
            }
            if (i + 1 < a.length && a[i - 1] < a[i + 1]) {
                gapPointR = i;
            } else {
                gapPointR = -1;
            }
            if (i - 2 >= 0 && a[i - 2] < a[i]) {
                gapPointL = i - 1;
            } else {
                gapPointL = -1;
            }
            prevCurMax = curMax;
            curMax = 1;

        }
        if (gapPointR != -1) {
            globalSMax = max(globalSMax, prevCurMax + curMax - 1);
        }
        if (gapPointL != -1) {
            globalSMax = max(globalSMax, prevCurMax + curMax - 1);
        }
        return max(globalSMax, curMax);
    }

    public static class FastScanner {
        StringTokenizer tok = new StringTokenizer("");
        BufferedReader in;

        public FastScanner() {
            in = new BufferedReader(new InputStreamReader(System.in));
        }

        public String next() throws IOException {
            while (!tok.hasMoreElements())
                tok = new StringTokenizer(in.readLine());
            return tok.nextToken();
        }

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

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