Consider a 3D scene with OXYZ coordinate system. Axis OX points to the right, axis OY points up, and axis OZ points away from you. There is a number of rectangular windows on the scene. The plane of each window is parallel to OXY , its sides are parallel to OX and OY . All windows are situated at different depths on the scene (different coordinates z > 0).
A gunman with a rifle moves along OX axis (y = 0 and z = 0). He can shoot a bullet in a straight line.
His goal is to shoot a single bullet through all the windows. Just touching a window edge is enough.
Your task is to determine how to make such shot.
Input
There are several test cases in the input. The first line of each case contains a single integer number n (2 ≤ n ≤ 100) --- the number of windows on the scene. The following n lines describe the windows. Each line contains five integer numbers x 1i , y 1i , x 2i , y 2i , z i (0 < x 1i , y 1i , x 2i , y 2i , z i < 1000). Here (x 1i , y 1i , z i ) are coordinates of the bottom left corner of the window, and (x 2i , y 2i , z i ) are coordinates of the top right corner of the window (x 1i < x 2i , y 1i < y 2i ). Windows are ordered by z coordinate (z i > z i-1 for 2 ≤ i ≤ n).
Output
Output a single word "UNSOLVABLE" if the gunman cannot reach the goal of shooting a bullet through all the windows.
Otherwise, on the first line output a word "SOLUTION". On the next line output x coordinate of the point from which the gunman must fire a bullet. On the following n lines output x, y, z coordinates of the points where the bullet goes through the consecutive windows. All coordinates in the output file must be printed with six digits after decimal point.
Sample Input
3
1 3 5 5 3
1 2 5 7 5
5 2 7 6 6
3
2 1 5 4 1
3 5 6 8 2
4 3 8 6 4
Sample Output
SOLUTION
-1.000000
2.000000 3.000000 3.000000
4.000000 5.000000 5.000000
5.000000 6.000000 6.000000
UNSOLVABLE
