Time Limit:1000ms Memory Limit:65536KB

Description

Given a triangle ABC and a point O in the triangle or on the edge of the triangle.
Link OA, OB, OC, we obtain three small triangles : OBC, OCA, OAB
we say that (S_OBC/S, S_OCA/S, S_OAB/S) is the area coordinates of O, where S
is the area of triangle ABC, and S_OBC is the area of triangle OBC, and
S_OCA, S_OAB are similar
Given A,B,C, and the area coordinates of O, you are expected to calculate the rectangular coordinate of O.

Input

One test case.
The first line is 6 float number Ax Ay Bx By Cx Cy, where (Ax, Ay) is the coordinates of point A
and (Bx, By), (Cx, Cy) are similar.
ABC is in a counter-clockwise order.
The six number are in the range of [-1000 1000]
In each of the next lines, there are three float number l1, l2, l3 which are the area coordinates
of O, and you are expected to calculate the rectangular coordinates of it.
O is in ABC or on the edge of ABC.

Output

For each O, output the rectangular coordiates of it.
Accurate to two decimal places.

0 0 0 1 1 0
1.00 0.00 0.00

0.00 0.00

Hint

Do not output -0.00.
The accuracy is 1e-6.

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