Buy the String

You are given four integers n, c_0, c_1 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 c_0 coins, to buy the character 1 you should pay c_1 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, c_{0}, c_{1}, h (1 ≤ n, c_{0}, c_{1}, 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.

inputFormat

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, c_{0}, c_{1}, h (1 ≤ n, c_{0}, c_{1}, h ≤ 1000).

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

outputFormat

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.

样例

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

3
52
5
10
16
22

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