Problem: You are given an angle 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} = ang or report that there is no such n-gon.

<image>

If there are several answers, print the minimal one. It is guarantied that if answer exists then it doesn't exceed 998244353.

Input

The first line contains single integer T (1 ≤ T ≤ 180) — the number of queries. 

Each of the next T lines contains one integer ang (1 ≤ ang < 180) — the angle measured in degrees. 

Output

For each query print single integer n (3 ≤ n ≤ 998244353) — minimal possible number of vertices in the regular n-gon or -1 if there is no such n.

Example

Input


4
54
50
2
178


Output


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).

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
public class C {
   public static void main(String[] args) {
      Scanner sc = new Scanner(System.in);
      
      int t = sc.nextInt();
      for(int i = 0; i < t; i++) {
         int angle = sc.nextInt();
         
         int g = gcd(180, angle);
         int a1 = 180 / g;
         int a2 = angle / g;
         
         if(a1 - a2 < 2)
            System.out.println(2 * a1);
         else
            System.out.println(a1);
      }
   }
   
   public static int gcd(int a, int b) {
      if(b == 0)
         return a;
      return gcd(b, a % b);
   }
}