Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

B. Messages

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThere are *n* incoming messages for Vasya. The *i*-th message is going to be received after *t*_{i} minutes. Each message has a cost, which equals to *A* initially. After being received, the cost of a message decreases by *B* each minute (it can become negative). Vasya can read any message after receiving it at any moment of time. After reading the message, Vasya's bank account receives the current cost of this message. Initially, Vasya's bank account is at 0.

Also, each minute Vasya's bank account receives *C*·*k*, where *k* is the amount of received but unread messages.

Vasya's messages are very important to him, and because of that he wants to have all messages read after *T* minutes.

Determine the maximum amount of money Vasya's bank account can hold after *T* minutes.

Input

The first line contains five integers *n*, *A*, *B*, *C* and *T* (1 ≤ *n*, *A*, *B*, *C*, *T* ≤ 1000).

The second string contains *n* integers *t*_{i} (1 ≤ *t*_{i} ≤ *T*).

Output

Output one integer — the answer to the problem.

Examples

Input

4 5 5 3 5

1 5 5 4

Output

20

Input

5 3 1 1 3

2 2 2 1 1

Output

15

Input

5 5 3 4 5

1 2 3 4 5

Output

35

Note

In the first sample the messages must be read immediately after receiving, Vasya receives *A* points for each message, *n*·*A* = 20 in total.

In the second sample the messages can be read at any integer moment.

In the third sample messages must be read at the moment T. This way Vasya has 1, 2, 3, 4 and 0 unread messages at the corresponding minutes, he gets 40 points for them. When reading messages, he receives (5 - 4·3) + (5 - 3·3) + (5 - 2·3) + (5 - 1·3) + 5 = - 5 points. This is 35 in total.

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Oct/18/2019 18:15:37 (f2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|