Strange Instructions
Description
Dasha has $10^{100}$ coins. Recently, she found a binary string $s$ of length $n$ and some operations that allows to change this string (she can do each operation any number of times):
- Replace substring 00 of $s$ by 0 and receive $a$ coins.
- Replace substring 11 of $s$ by 1 and receive $b$ coins.
- Remove 0 from any position in $s$ and pay $c$ coins.
It turned out that while doing this operations Dasha should follow the rule:
- It is forbidden to do two operations with the same parity in a row. Operations are numbered by integers $1$-$3$ in the order they are given above.
Please, calculate what is the maximum profit Dasha can get by doing these operations and following this rule.
The first line contains a single integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases.
The first line of each test case contains four integers $n$, $a$, $b$, $c$ ($1 \leq n \leq 10^5, 1 \leq a, b, c \leq 10^9$).
The second line of each test case contains a binary string $s$ of length $n$.
It is guaranteed that the total sum of $n$ over all test cases doesn't exceed $2 \cdot 10^5$.
For each test case print the answer.
Input
The first line contains a single integer $t$ ($1 \leq t \leq 10^4$) — the number of test cases.
The first line of each test case contains four integers $n$, $a$, $b$, $c$ ($1 \leq n \leq 10^5, 1 \leq a, b, c \leq 10^9$).
The second line of each test case contains a binary string $s$ of length $n$.
It is guaranteed that the total sum of $n$ over all test cases doesn't exceed $2 \cdot 10^5$.
Output
For each test case print the answer.
Samples
3
5 2 2 1
01101
6 4 3 5
110001
6 3 2 1
011110
3
11
4
Note
In the first test case one of the optimal sequences of operations is 01101 $\rightarrow$ 0101 $\rightarrow$ 011 $\rightarrow$ 01. This sequence of operations consists of operations $2$, $3$ and $2$ in this order. It satisfies all rules and gives profit $3$. It can be shown that it is impossible to achieve higher profit in this test case, so the answer is $3$.
In the second test case one of the optimal sequences of operations is 110001 $\rightarrow$ 11001 $\rightarrow$ 1001 $\rightarrow$ 101.
In the third test case one of the optimal sequences of operations is 011110 $\rightarrow$ 01110 $\rightarrow$ 1110 $\rightarrow$ 110 $\rightarrow$ 11 $\rightarrow$ 1.