The life goes up and down, just like nice sequences. Sequence t1, t2, ..., tn is called nice if the following two conditions are satisfied: 

  * ti < ti + 1 for each odd i < n; 
  * ti > ti + 1 for each even i < n. 



For example, sequences (2, 8), (1, 5, 1) and (2, 5, 1, 100, 99, 120) are nice, while (1, 1), (1, 2, 3) and (2, 5, 3, 2) are not.

Bear Limak has a sequence of positive integers t1, t2, ..., tn. This sequence is not nice now and Limak wants to fix it by a single swap. He is going to choose two indices i < j and swap elements ti and tj in order to get a nice sequence. Count the number of ways to do so. Two ways are considered different if indices of elements chosen for a swap are different.

Input

The first line of the input contains one integer n (2 ≤ n ≤ 150 000) — the length of the sequence.

The second line contains n integers t1, t2, ..., tn (1 ≤ ti ≤ 150 000) — the initial sequence. It's guaranteed that the given sequence is not nice.

Output

Print the number of ways to swap two elements exactly once in order to get a nice sequence.

Examples

Input

5
2 8 4 7 7


Output

2


Input

4
200 150 100 50


Output

1


Input

10
3 2 1 4 1 4 1 4 1 4


Output

8


Input

9
1 2 3 4 5 6 7 8 9


Output

0

Note

In the first sample, there are two ways to get a nice sequence with one swap: 

  1. Swap t2 = 8 with t4 = 7. 
  2. Swap t1 = 2 with t5 = 7. 



In the second sample, there is only one way — Limak should swap t1 = 200 with t4 = 50.
import java.io.*;
import java.util.*;

public class C_new {

	BufferedReader br;
	PrintWriter out;
	StringTokenizer st;
	boolean eof;

	void solve() throws IOException {
		int n = nextInt();
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = nextInt();
		}

		List<Integer> bad = new ArrayList<>();

		int[] arrBad = new int[n - 1];
		int totBad = 0;

		for (int i = 0; i < n - 1; i++) {
			if ((i % 2 == 0 && a[i] >= a[i + 1])
					|| (i % 2 == 1 && a[i] <= a[i + 1])) {
				bad.add(i);
				totBad++;
				arrBad[i] = 1;
			}
		}

		if (bad.size() > 4) {
			out.println(0);
			return;
		}
		
		HashSet<Long> set = new HashSet<>();

		int ret = 0;

		for (int i1 = 0; i1 < bad.size(); i1++) {
			for (int ii = 0; ii < 2; ii++) {

				int x = bad.get(i1) + ii;

				for (int y = 0; y < n; y++) {
					
					if (x == y) {
						continue;
					}
					
					int low = Math.min(x, y);
					int high = Math.max(x, y);
					
					long hash = (long)low * n + high;
					if (set.contains(hash)) {
						continue;
					}
					set.add(hash);
					
					
					int tmp = a[low];
					a[low] = a[high];
					a[high] = tmp;
					
					int nowBad = totBad;

					if (low != 0) {
						int i = low - 1;
						int here;
						if ((i % 2 == 0 && a[i] >= a[i + 1])
								|| (i % 2 == 1 && a[i] <= a[i + 1]))
							here = 1;
						else
							here = 0;
						nowBad += here - arrBad[i];
					}
					
					if (low != n - 1) {
						int i = low;
						int here;
						if ((i % 2 == 0 && a[i] >= a[i + 1])
								|| (i % 2 == 1 && a[i] <= a[i + 1]))
							here = 1;
						else
							here = 0;
						nowBad += here - arrBad[i];
					}
					
					
					if (high != low + 1) {
						int i = high - 1;
						int here;
						if ((i % 2 == 0 && a[i] >= a[i + 1])
								|| (i % 2 == 1 && a[i] <= a[i + 1]))
							here = 1;
						else
							here = 0;
						nowBad += here - arrBad[i];
					}
					
					if (high != n - 1) {
						int i = high;
						int here;
						if ((i % 2 == 0 && a[i] >= a[i + 1])
								|| (i % 2 == 1 && a[i] <= a[i + 1]))
							here = 1;
						else
							here = 0;
						nowBad += here - arrBad[i];
					}
					
					if (nowBad == 0) {
						ret++;
					}
					
					tmp = a[x];
					a[x] = a[y];
					a[y] = tmp;

				}
			}
		}

		out.println(ret);
	}

	C_new() throws IOException {
		br = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
		solve();
		out.close();
	}

	public static void main(String[] args) throws IOException {
		new C_new();
	}

	String nextToken() {
		while (st == null || !st.hasMoreTokens()) {
			try {
				st = new StringTokenizer(br.readLine());
			} catch (Exception e) {
				eof = true;
				return null;
			}
		}
		return st.nextToken();
	}

	String nextString() {
		try {
			return br.readLine();
		} catch (IOException e) {
			eof = true;
			return null;
		}
	}

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

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

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