653_C. Bear and Up-Down
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.
```python
def main():
    n, l = int(input()), list(map(int, input().split()))
    if not (n & 1):
        l.append(0)
    l.append(150001)
    a, b, fails, res = 0, 150001, [], 0
    for i, c in enumerate(l, -1):
        if i & 1:
            if a >= b or b <= c:
                if len(fails) > 5:
                    print(0)
                    return
                fails.append(i)
        else:
            if a <= b or b >= c:
                if len(fails) > 5:
                    print(0)
                    return
                fails.append(i)
        a, b = b, c
    check = compile("and".join(
        "(l[{:n}]{:s}l[{:n}]{:s}l[{:n}])".format(i - 1, "><"[i & 1], i, "<>"[i & 1], i + 1) for i in fails),
                   "<string>", "eval")
    for i in fails:
        a = l[i]
        for j in range(n):
            l[i], l[j] = l[j], a
            if eval(check) and ((l[j - 1] < l[j] > l[j + 1]) if j & 1 else (l[j - 1] > l[j] < l[j + 1])):
                res += 1 if j in fails else 2
            l[j] = l[i]
        l[i] = a
    print(res // 2)


if __name__ == '__main__':
    main()



# Made By Mostafa_Khaled
```