Bear and Up-Down

2000ms

262144K

Description:

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

t_i < t_i + 1 for each odd i < n;
t_i > t_i + 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, ..., t_n. 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 t_i and t_j 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, ..., t_n (1 ≤ t_i ≤ 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.

Sample Input:

5
2 8 4 7 7

Sample Output:

Sample Input:

4
200 150 100 50

Sample Output:

Sample Input:

10
3 2 1 4 1 4 1 4 1 4

Sample Output:

Sample Input:

9
1 2 3 4 5 6 7 8 9

Sample Output:

Note:

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

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

In the second sample, there is only one way — Limak should swap t₁ = 200 with t₄ = 50.

Informação

Provedor Codeforces

Código CF653C