402388: GYM100741 J Empty Circle

You are given a set of n points S = {p₁, p₂, ..., p_n} on the plane. A triple (p_i, p_j, p_k) 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!

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 x_i and y_i, the coordinates of p_i ( - 10⁴ ≤ x_i, y_i ≤ 10⁴). No two given points will be equal.

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.

4
0 1
0 0
-1 -1
1 -1

Yes
3 1 2

3
-1 -1
0 0
1 1

No

4
-2 -2
2 -2
-2 2
2 2

Yes
1 3 2