write a go solution for Description:
This is an interactive problem.

Khanh has n points on the Cartesian plane, denoted by a_1,a_2,ldots,a_n. All points' coordinates are integers between -10^9 and 10^9, inclusive. No three points are collinear. He says that these points are vertices of a convex polygon; in other words, there exists a permutation p_1,p_2,ldots,p_n of integers from 1 to n such that the polygon a_p_1a_p_2ldotsa_p_n is convex and vertices are listed in counter-clockwise order.

Khanh gives you the number n, but hides the coordinates of his points. Your task is to guess the above permutation by asking multiple queries. In each query, you give Khanh 4 integers t, i, j, k; where either t=1 or t=2; and i, j, k are three distinct indices from 1 to n, inclusive. In response, Khanh tells you:

- if t=1, the area of the triangle a_ia_ja_k multiplied by 2.
- if t=2, the sign of the cross product of two vectors overarrowa_ia_j and overarrowa_ia_k.

Recall that the cross product of vector overarrowa=(x_a,y_a) and vector overarrowb=(x_b,y_b) is the integer x_a*y_b-x_b*y_a. The sign of a number is 1 it it is positive, and -1 otherwise. It can be proven that the cross product obtained in the above queries can not be 0.

You can ask at most 3*n queries.

Please note that Khanh fixes the coordinates of his points and does not change it while answering your queries. You do not need to guess the coordinates. In your permutation a_p_1a_p_2ldotsa_p_n, p_1 should be equal to 1 and the indices of vertices should be listed in counter-clockwise order.

Input Format:
None

Output Format:
None

Note:
The image below shows the hidden polygon in the example:

The interaction in the example goes as below:

- Contestant reads n=6.
- Contestant asks a query with t=1, i=1, j=4, k=6.
- Jury answers 15. The area of the triangle A_1A_4A_6 is 7.5. Note that the answer is two times the area of the triangle.
- Contestant asks a query with t=2, i=1, j=5, k=6.
- Jury answers -1. The cross product of overarrowA_1A_5=(2,2) and overarrowA_1A_6=(4,1) is -2. The sign of -2 is -1.
- Contestant asks a query with t=2, i=2, j=1, k=4.
- Jury answers 1. The cross product of overarrowA_2A_1=(-5,2) and overarrowA_2A_4=(-2,-1) is 1. The sign of 1 is 1.
- Contestant says that the permutation is (1,3,4,2,6,5).. Output only the code with no comments, explanation, or additional text.