You are given four integers n, c0, c1 and h and a binary string s of length n.

A binary string is a string consisting of characters 0 and 1.

You can change any character of the string s (the string should be still binary after the change). You should pay h coins for each change.

After some changes (possibly zero) you want to buy the string. To buy the string you should buy all its characters. To buy the character 0

?you should pay c0 coins, to buy the character 1 you should pay c1 coins.

Find the minimum number of coins needed to buy the string.

Input

The first line contains a single integer t (1≤t≤10) — the number of test cases. Next 2t lines contain descriptions of test cases.

The first line of the description of each test case contains four integers n, c0, c1, h (1≤n,c0,c1,h≤1000).

The second line of the description of each test case contains the binary string s of length n.

Output

For each test case print a single integer — the minimum number of coins needed to buy the string.

Example

input

6

3 1 1 1

100

5 10 100 1

01010

5 10 1 1

11111

5 1 10 1

11111

12 2 1 10

101110110101

2 100 1 10

00

output

3

52

5

10

16

22

Note

In the first test case, you can buy all characters and pay 3 coins, because both characters 0 and 1 costs 1 coin.

In the second test case, you can firstly change 2-nd and 4-th symbols of the string from 1 to 0 and pay 2 coins for that. Your string will be 00000. After that, you can buy the string and pay 5?10=50

?coins for that. The total number of coins paid will be 2+50=52.

給定字符串，01字符，其中買0字符的要花c0元，買1字符的要花c1元，如果把0跟1交換的話，要花h元，問如果能最小化買了這個字符串的金額。

主要是判斷2個參數(shù)h+c0跟c1的關(guān)系，還有h+c1跟c0的關(guān)系，即可。

剩下就是hashmap 處理即可；（當然也可用變量存儲）