Bear and Up-Down

题意翻译

人生起起落落，就像令人愉快的序列。只要满足了以下两种条件，序列$t1$,$t2$,...,$tn$就叫做令人愉快的： - 对于每一个奇数$i（i<n）$有$ti<ti+1$; - 对于每一个偶数$i（i<n）$有$ti>ti+1$; 举个例子，序列$(2,8)$,$(1,5,1)$和$(2,5,1,100,99,120)$就是令人愉快的，但是$(1,1)$,$(1,2,3)$和$(2,5,3,2)$就不是。 Bear Limak有一个正整数序列$t1$,$t2$,...,$tn$。现在这个序列**不是令人愉快的**，Limak想要通过一次交换来修改它。他将要选择两个指数$i<j$然后交换他们的元素$ti$和$tj$从而得到一个令人愉快的序列。数数有多少种方法可以得到。如果交换的两个元素的指数不同则认为这是两种不同的方法。 **输入格式** 输入的第一行包含一个整数$n$$(2≤n≤150000)$代表虚列的长度。 第二行包含$n$个整数$t1$,$t2$,...,$tn$$(1≤ti≤150000)$代表初始的序列。可以保证的是所给的序列一定不令人愉快。 **输出格式** 输出想要得到一个令人愉快的序列有多少种方法来交换两个元素。 **提示/说明** 在第一个样例中，有两种方式通过一次交换得到一个令人满意的序列： 1. 交换$t2=8$和$t4=7$。 1. 交换$t1=2$和$t5=7$。 在第二个样例中，只有一种方式—Limak应该交换$t1=200$和$t4=50$。

题目描述

The life goes up and down, just like nice sequences. Sequence $ t_{1},t_{2},...,t_{n} $ is called nice if the following two conditions are satisfied: - $ t_{i}&lt;t_{i+1} $ for each odd $ i&lt;n $ ; - $ t_{i}&gt;t_{i+1} $ for each even $ i&lt;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 $ t_{1},t_{2},...,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&lt;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.

输入输出格式

输入格式

The first line of the input contains one integer $ n $ ( $ 2<=n<=150000 $ ) — the length of the sequence. The second line contains $ n $ integers $ t_{1},t_{2},...,t_{n} $ ( $ 1<=t_{i}<=150000 $ ) — the initial sequence. It's guaranteed that the given sequence is not nice.

输出格式

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

输入输出样例

输入样例 #1

5
2 8 4 7 7

输出样例 #1

2

输入样例 #2

4
200 150 100 50

输出样例 #2

1

输入样例 #3

10
3 2 1 4 1 4 1 4 1 4

输出样例 #3

8

输入样例 #4

9
1 2 3 4 5 6 7 8 9

输出样例 #4

0

说明

In the first sample, there are two ways to get a nice sequence with one swap: 1. Swap $ t_{2}=8 $ with $ t_{4}=7 $ . 2. Swap $ t_{1}=2 $ with $ t_{5}=7 $ . In the second sample, there is only one way — Limak should swap $ t_{1}=200 $ with $ t_{4}=50 $ .