codeforces#P1096C. Polygon for the Angle
Polygon for the Angle
Description
You are given an angle $\text{ang}$.
The Jury asks You to find such regular $n$-gon (regular polygon with $n$ vertices) that it has three vertices $a$, $b$ and $c$ (they can be non-consecutive) with $\angle{abc} = \text{ang}$ or report that there is no such $n$-gon.
If there are several answers, print the minimal one. It is guarantied that if answer exists then it doesn't exceed $998244353$.
The first line contains single integer $T$ ($1 \le T \le 180$) — the number of queries.
Each of the next $T$ lines contains one integer $\text{ang}$ ($1 \le \text{ang} < 180$) — the angle measured in degrees.
For each query print single integer $n$ ($3 \le n \le 998244353$) — minimal possible number of vertices in the regular $n$-gon or $-1$ if there is no such $n$.
Input
The first line contains single integer $T$ ($1 \le T \le 180$) — the number of queries.
Each of the next $T$ lines contains one integer $\text{ang}$ ($1 \le \text{ang} < 180$) — the angle measured in degrees.
Output
For each query print single integer $n$ ($3 \le n \le 998244353$) — minimal possible number of vertices in the regular $n$-gon or $-1$ if there is no such $n$.
Samples
4
54
50
2
178
10
18
90
180
Note
The answer for the first query is on the picture above.
The answer for the second query is reached on a regular $18$-gon. For example, $\angle{v_2 v_1 v_6} = 50^{\circ}$.
The example angle for the third query is $\angle{v_{11} v_{10} v_{12}} = 2^{\circ}$.
In the fourth query, minimal possible $n$ is $180$ (not $90$).