F. Fountain at UFBA
time limit per test
0.5 seconds
memory limit per test
1024 megabytes
input
standard input
output
standard output

The GruPro (Grupo de Programaçao da UFBA) wants to install a new drinking fountain on the Ondina campus, somewhere among the wooded paths between the Instituto de Computação and the Restaurante Universitário.

The campus map is an integer grid. There are $$$N$$$ benches, and the $$$i$$$-th bench sits at integer coordinates $$$(x_i, y_i)$$$. To be fair to everyone, the students decided the fountain must be placed exactly halfway between two benches: that is, at the midpoint of some pair of distinct benches $$$i$$$ and $$$j$$$, $$$$$$\left( \frac{x_i + x_j}{2},\ \frac{y_i + y_j}{2} \right). $$$$$$

Underground pipes can only reach points with integer coordinates, so the chosen midpoint must land exactly on a grid point.

Help the GruPro pick two benches whose midpoint is a valid spot for the fountain, or tell them it is impossible.

Input

The first line contains a single integer $$$N$$$ ($$$2 \leq N \leq 10^{5}$$$), the number of benches.

Each of the next $$$N$$$ lines contains two integers $$$x_i$$$ and $$$y_i$$$ ($$$-10^{6} \leq x_i, y_i \leq 10^{6}$$$), the coordinates of the $$$i$$$-th bench. No two benches share the same position.

Output

If there is a pair of distinct benches whose midpoint has integer coordinates, print two integers $$$i$$$ and $$$j$$$ ($$$1 \leq i, j \leq N$$$, $$$i \neq j$$$): the indices of two such benches. If several pairs work, print any of them.

If no such pair exists, print a single integer $$$-1$$$.

Examples
Input
4
0 0
1 0
2 1
4 2
Output
1 4
Input
3
0 0
1 0
0 1
Output
-1
Note

Explanation for example 1

Benches $$$1$$$ and $$$4$$$ are at $$$(0,0)$$$ and $$$(4,2)$$$. Their midpoint is $$$(2,1)$$$, which has integer coordinates, so the fountain can be placed there. Benches $$$1$$$ and $$$3$$$ would also work; any valid pair is accepted.

Explanation for example 2

Checking the three possible pairs, every midpoint has at least one half-integer coordinate. For example, the midpoint of benches $$$1$$$ and $$$2$$$ is $$$(0.5,\ 0)$$$. Since no pair gives an integer point, the answer is $$$-1$$$.