Description

一个长度为n的记账单，+表示存￥1，-表示取￥1。现在发现记账单有问题。一开始本来已经存了￥p，并且知道最后账户上还有￥q。你要把记账单修改正确，使得 1：账户永远不会出现负数； 2：最后账户上还有￥q。你有2种操作： 1：对某一位取反，耗时x； 2：把最后一位移到第一位，耗时y。

Input

The first line contains 5 integers n, p, q, x and y (1  n  1000000, 0  p;q  1000000, 1  x;y  1000), separated by single spaces and denoting respectively: the number of transactions done by Byteasar, initial and final account balance and the number of seconds needed to perform a single turn (change of sign) and move of transaction to the beginning. The second line contains a sequence of n signs (each a plus or a minus), with no spaces in-between. 1 ≤ n ≤ 1000000, 0 ≤ p ,q ≤ 1000000, 1 ≤x,y ≤ 1000)

Output

修改消耗的时间

Sample Input

Sample Output

Hint

Source