J. Empty Circle
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a set of n points S = {p1, p2, ..., pn} on the plane. A triple (pi, pj, pk) is called good if no point in S is strictly inside the circumference of these three points. If it is possible, find a good triple!

Input

The first line contains an integer n, the number of the points (3 ≤ n ≤ 106). The i-th of the next n lines contains two integer numbers xi and yi, the coordinates of pi ( - 104 ≤ xi, yi ≤ 104). No two given points will be equal.

Output

If a good triple exists, output "Yes" in the first line. In the next line output three space-separated integers, the numbers of the three points as they appeared in the input.

If no good triple exists, output "No" in a single line.

Examples
Input
4
0 1
0 0
-1 -1
1 -1
Output
Yes
3 1 2
Input
3
-1 -1
0 0
1 1
Output
No
Input
4
-2 -2
2 -2
-2 2
2 2
Output
Yes
1 3 2