Problem Statement

There is an infinitely large triangular grid, as shown below. Each point with integer coordinates contains a lamp.

Initially, only the lamp at ~(X, 0)~ 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~ .

Constraints

• ~1 \leq N \leq 10^5~
• ~-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~ .

Input

Input is given from Standard Input in the following format:

~N~

~x_1~ ~y_1~

~:~

~x_N~ ~y_N~

Output

Print ~X~ .

Sample Input 1

4
-2 1
-2 2
0 1
1 0

Sample Output 1

-1

The following picture shows one possible sequence of operations: