You are given a binary array (array consists of \(0's\) and \(1's\)) \(A\) that contains \(N\) elements. You can perform the following operation as many time as you like:

1.  Choose any index  \(1\leq i \leq N\) and if it is currently 0, then convert it to 1 for C₀₁ coins.
2.  Choose any index  \(1\leq i \leq N\) and if it is currently 1, then convert it to 0 for C₁₀ coins.

Your task is to transform the given array into a special array that for every index \(1 \leq i < N\), \(A_i \land A_{i+1} = 1\).

Here, \(\land\) denotes XOR.

Input format

• The first line contains \(T\) the number of test cases.
• The first line of each test case contains three space-separated integers \(N\), C₀₁ and C₁₀.
• The second line consists of \(N\) space-separated integers of array \(A\).

Output format

For each test case, print one line denoting the minimum cost to transform array \(A\) into a special array.

Constraints

\(1 \leq T \leq 100\)

\(1 \leq N \leq 10000\)

\(0 \leq A[i] \leq 1 \forall i \in [1,N]\)

\(1 \leq C01,C10 \leq 1e9\)