You are standing at point (x1,y1) in an infinite 2D plane. You have to go to point (x2,y2) in minimum cost.
The allowed moves are :
(x,y) -> (x,y-1) or (x,y+1) or (x-1,y) or (x+1,y), costing an amount A.
(x,y) -> (x-1,y-1) or (x-1,y+1) or (x+1,y-1) or (x+1,y+1), costing an amount B.
Input Format
The first line contains the number T.
The following T lines contain 6 numbers each : x1, y1, x2, y2, A, B.
Output Format
Output the answer for each testcase in a newline.
Constraints
1<=T<=10000
-1e9<=x1,y1,x2,y2<=1e9
1<=A,B<=1e9
Testcase 1: The optimal path is (0,0) -> (1,1) with cost 6.
Testcase 2: The optimal path is (0,0) -> (0,1) -> (1,1) with cost 2.