CF1096C.Polygon for the Angle

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 $998244353$.

给你一个角度 $\text{ang}$。

评测组要求你找出一个正 $n$ 边形（具有 $n$ 个顶点的正多边形），使得该正 $n$ 边形中存在三个顶点 $a$、$b$ 和 $c$（它们不必相邻），满足 $\angle{abc} = \text{ang}$；若不存在这样的正 $n$ 边形，则报告无解。

若存在多个解，请输出最小的 $n$。题目保证：若解存在，则其值不超过 $998244353$。

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 $\text{ang}$ ($1 \le \text{ang} \lt 180$) — the angle measured in degrees.

第一行包含一个整数 $T$（$1 \le T \le 180$）—— 查询次数。

接下来的 $T$ 行，每行包含一个整数 $\text{ang}$（$1 \le \text{ang} \lt 180$）—— 以度为单位测量的角度。

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 $n$.

对于每个查询，输出一个整数 $n$（$3 \le n \le 998244353$）——即满足条件的正 $n$ 边形的最少顶点数；若不存在这样的 $n$，则输出 $-1$。

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 $90$).

第一个查询的答案如上图所示。

第二个查询的答案在一个正 $18$ 边形中达到。例如，$\angle{v_2 v_1 v_6} = 50^{\circ}$。

第三个查询的示例角度为 $\angle{v_{11} v_{10} v_{12}} = 2^{\circ}$。

在第四个查询中，最小可能的 $n$ 是 $180$（而非 $90$）。