Cut frame

Rectangular frame was divided into N pieces. Each piece can be either a line segment, or "corner" - two segments, joined at right angles.

According to the lengths required to restore the original frame, or determine that it is impossible. The pieces can be rotated, but can not reflect. You have to use all the pieces.

Input

The input file contains the number of pieces N, followed by Npairs of integers a_i b_i, describing the length of two segments of "corner" i-th piece. If a piece is a segment, then a_i = 0 or b_i = 0.

Output

Output file must contain two positive integers W H — the width and height of the frame, with W ≥ H. If the solution does not exist, it should give the number of −1. ЕIf making a few, must issue a decision with the maximum value of W.

Examples