You are given an array $$A$$ which consists of $$N$$ elements. Each element of array is either zero or one. Your task is to convert the given array into a good array with a minimum cost.

Good array: In a good array, select any subarray of even length $$M$$ and the sum of elements in the subarray will be $$M/2$$.

In order to transform an array to good array, you can perform the following two operations as many times as you want:

1.  Choose any index $$1≤i≤N$$ and if it is currently 0, then convert it to 1 for X coins.
2.  Choose any index $$1≤i≤N$$ and if it is currently 1, then convert it to 0 for Y coins.

Your task is to minimize the cost of transformation of an array to good array.

Input format

• The first line contains $$T$$ denoting the number of test cases.
• The first line of each test case contains three space-separated integers $$N$$, $$X$$, and $$Y$$.
• The second line of each test case 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 good array.

Constraints

\(1 \leq T \leq 100\)

\(1 \leq N \leq 10^4\)

\(0 \leq A_i \leq 1\)

\(1 \leq X,Y \leq 10^9\)