A14847. Strange Instructions

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):

1. Replace substring 00 of $s$ by 0 and receive $a$ coins.
2. Replace substring 11 of $s$ by 1 and receive $b$ coins.
3. 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.

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.