Score : 1000 points
Problem Statement
Red bold fonts show the difference from C1.
There is an infinitely large triangular grid, as shown below. Each point with integer coordinates contains a lamp.
Initially, only the lamp at (X, Y) was on, and all other lamps were off. Then, Snuke performed the following operation zero or more times:
- Choose two integers x and y. Toggle (on to off, off to on) the following three lamps: (x, y), (x, y+1), (x+1, y).
After the operations, N lamps (x_1, y_1), \cdots, (x_N, y_N) are on, and all other lamps are off. Find X and Y.
Constraints
- 1 \leq N \leq 10^4
- -10^{17} \leq x_i, y_i \leq 10^{17}
- (x_i, y_i) are pairwise distinct.
- The input is consistent with the statement, and you can uniquely determine X and Y.
Input
Input is given from Standard Input in the following format:
N x_1 y_1 : x_N y_N
Output
Print X and Y, separated by a space.
Sample Input 1
4 -2 1 -2 2 0 1 1 0
Sample Output 1
-1 0
The following picture shows one possible sequence of operations:
