B. Square Locator
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

There is a square $$$ABCD$$$ whose vertices have integer coordinates, with $$$A$$$ on the positive $$$y$$$-axis.

You are given the squared distances $$$AO^2$$$, $$$BO^2$$$, $$$CO^2$$$, $$$DO^2$$$, where $$$O(0,0)$$$ is the origin. Find the vertices of the square.

Input

The only line of each test contains four integers $$$AO^2$$$, $$$BO^2$$$, $$$CO^2$$$, $$$DO^2$$$ ($$$1 \leq AO^2, BO^2, CO^2, DO^2 \leq 10^{18}$$$) — the squares of the distances of the vertices of the square to the origin.

Output

Output one line containing seven space-separated integers $$$A_y$$$, $$$B_x$$$, $$$B_y$$$, $$$C_x$$$, $$$C_y$$$, $$$D_x$$$, $$$D_y$$$, representing the coordinates of the vertices of the square $$$A(0, A_y)$$$, $$$B(B_x, B_y)$$$, $$$C(C_x, C_y)$$$, $$$D(D_x, D_y)$$$.

The input is given in such a way that such integers exist. If there are multiple possible answers, print any of them.

Example
Input
36 5 10 41
Output
6 -1 2 3 1 4 5
Note

The first test case is pictured below.