Secret Letters
Description
Little W and Little P decided to send letters to each other regarding the most important events during a day. There are $n$ events during a day: at time moment $t_i$ something happens to the person $p_i$ ($p_i$ is either W or P, denoting Little W and Little P, respectively), so he needs to immediately send a letter to the other person. They can send a letter using one of the two ways:
- Ask Friendly O to deliver the letter directly. Friendly O takes $d$ acorns for each letter.
- Leave the letter at Wise R's den. Wise R values free space, so he takes $c \cdot T$ acorns for storing a letter for a time segment of length $T$. The recipient can take a letter from Wise R either when he leaves his own letter at Wise R's den, or at time moment $t_{n + 1}$, when everybody comes to Wise R for a tea. It is not possible to take a letter from Wise R's den at other time moments. The friends can store as many letters at Wise R's den as they want, paying for each one separately.
Help the friends determine the minimum possible total cost of sending all letters.
The first line contains three integers $n, c, d$ ($1 \leq n \leq 10^5$, $1 \leq c \leq 10^2$, $1 \leq d \leq 10^8$) — the number of letters, the cost of storing a letter for one time unit at Wise R's den and the cost of delivering a letter via Friendly O.
The next $n$ describe the events. The $i$-th of them contains an integer $t_i$ and a character $p_i$ ($0 \leq t_i \leq 10^6$, $p_i$ is either W or P) — the time the $i$-th event happens and the person the event happens to.
The last line contains a single integer $t_{n + 1}$ ($0 \leq t_{n+1} \leq 10^6$) — the time when everybody comes to Wise R for a tea and takes all remaining letters.
It is guaranteed that $t_i < t_{i + 1}$ for all $i$ from $1$ to $n$.
Print a single integer — the minimum possible cost of delivery of all letters.
Input
The first line contains three integers $n, c, d$ ($1 \leq n \leq 10^5$, $1 \leq c \leq 10^2$, $1 \leq d \leq 10^8$) — the number of letters, the cost of storing a letter for one time unit at Wise R's den and the cost of delivering a letter via Friendly O.
The next $n$ describe the events. The $i$-th of them contains an integer $t_i$ and a character $p_i$ ($0 \leq t_i \leq 10^6$, $p_i$ is either W or P) — the time the $i$-th event happens and the person the event happens to.
The last line contains a single integer $t_{n + 1}$ ($0 \leq t_{n+1} \leq 10^6$) — the time when everybody comes to Wise R for a tea and takes all remaining letters.
It is guaranteed that $t_i < t_{i + 1}$ for all $i$ from $1$ to $n$.
Output
Print a single integer — the minimum possible cost of delivery of all letters.
Samples
5 1 4
0 P
1 W
3 P
5 P
8 P
10
16
10 10 94
17 W
20 W
28 W
48 W
51 P
52 W
56 W
62 P
75 P
78 P
87
916
Note
One of optimal solutions in the first example:
- At time moment 0 Little P leaves the letter at Wise R's den.
- At time moment 1 Little W leaves his letter at Wise R's den and takes Little P's letter. This letter is at the den from time moment 0 to time moment 1, it costs $1$ acorn.
- At time moment 3 Little P sends his letter via Friendly O, it costs $4$ acorns.
- At time moment 5 Little P leaves his letter at the den, receiving Little W's letter which storage costs 4 acorns.
- At time moment 8 Little P leaves one more letter at the den.
- At time moment 10 Little W comes to the den for a tea and receives the two letters, paying 5 and 2 acorns.
The total cost of delivery is thus $1 + 4 + 4 + 5 + 2 = 16$ acorns.