Cashier

定义一天的长度为$L$,每次休息的时间为$a$,有$n$个客人，$t_i$表示他在这一天到来的时间，$l_i$表示他到来以后持续占用的时间。保证$t_i+l_i<=t_{i+1}$。问最多能休息的次数。

Vasya has recently got a job as a cashier at a local store. His day at work is $ L $ minutes long. Vasya has already memorized $ n $ regular customers, the $ i $ -th of which comes after $ t_{i} $ minutes after the beginning of the day, and his service consumes $ l_{i} $ minutes. It is guaranteed that no customer will arrive while Vasya is servicing another customer. Vasya is a bit lazy, so he likes taking smoke breaks for $ a $ minutes each. Those breaks may go one after another, but Vasya must be present at work during all the time periods he must serve regular customers, otherwise one of them may alert his boss. What is the maximum number of breaks Vasya can take during the day?

The first line contains three integers $ n $ , $ L $ and $ a $ ( $ 0 \le n \le 10^{5} $ , $ 1 \le L \le 10^{9} $ , $ 1 \le a \le L $ ). The $ i $ -th of the next $ n $ lines contains two integers $ t_{i} $ and $ l_{i} $ ( $ 0 \le t_{i} \le L - 1 $ , $ 1 \le l_{i} \le L $ ). It is guaranteed that $ t_{i} + l_{i} \le t_{i + 1} $ and $ t_{n} + l_{n} \le L $ .

Output one integer — the maximum number of breaks.

2 11 3
0 1
1 1

3

0 5 2

2

1 3 2
1 2

0

In the first sample Vasya can take $ 3 $ breaks starting after $ 2 $ , $ 5 $ and $ 8 $ minutes after the beginning of the day. In the second sample Vasya can take $ 2 $ breaks starting after $ 0 $ and $ 2 $ minutes after the beginning of the day. In the third sample Vasya can't take any breaks.