Problem:
Score : 500 points

Problem Statement

In CODE FESTIVAL XXXX, there are N+1 participants from all over the world, including Takahashi.

Takahashi checked and found that the time gap (defined below) between the local times in his city and the i-th person's city was D_i hours.
The time gap between two cities is defined as follows. For two cities A and B, if the local time in city B is d o'clock at the moment when the local time in city A is 0 o'clock, then the time gap between these two cities is defined to be min(d,24-d) hours.
Here, we are using 24-hour notation.
That is, the local time in the i-th person's city is either d o'clock or 24-d o'clock at the moment when the local time in Takahashi's city is 0 o'clock, for example.

Then, for each pair of two people chosen from the N+1 people, he wrote out the time gap between their cities. Let the smallest time gap among them be s hours.

Find the maximum possible value of s.

Constraints

1 \leq N \leq 50

0 \leq D_i \leq 12

All input values are integers.

Input

Input is given from Standard Input in the following format:

N
D_1 D_2 ... D_N

Output

Print the maximum possible value of s.

Sample Input 1

3
7 12 8

Sample Output 1

4

For example, consider the situation where it is 7, 12 and 16 o'clock in each person's city at the moment when it is 0 o'clock in Takahashi's city. In this case, the time gap between the second and third persons' cities is 4 hours.

Sample Input 2

2
11 11

Sample Output 2

2

Sample Input 3

1
0

Sample Output 3

0

Note that Takahashi himself is also a participant.

Solution in C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>
#include <math.h>
#include <limits.h>
#include <assert.h>
#define FOR(i,a,n) for(i=(a);i<(n);i++)
#define swap(type,a,b) do{type t=a;a=b;b=t;}while(0)
#define MAX(a,b) (((a)>(b))?(a):(b))
#define MIN(a,b) (((a)<(b))?(a):(b))
#define ll long long
#define INF 100000000
#define MOD 1000000007
#define SIZE 100005
//#define LOCAL
#ifdef LOCAL
    #define DEBUG(...) printf(" "__VA_ARGS__)
#else
    #define DEBUG(...)
#endif /* LOCAL */
typedef struct{
	int t,num;
}City;
int comp(const void* a,const void* b){
	return ((City*)a)->t - ((City*)b)->t;
}
int d[50];
City city[100];
int used[50];
int n;
int check(int s){
	int now=s,cnt=0,i;
	memset(used,0,sizeof(used));
	FOR(i,0,2*n){
		if(city[i].t<now) continue;
		if(!used[city[i].num]){
			used[city[i].num]=1;
			cnt++;
			now=city[i].t+s;
		}
	}
	return cnt==n;
}
int main(void)
{
	int left,right,mid,i;
	scanf("%d",&n);
	FOR(i,0,n){
		scanf("%d",d+i);
		city[i*2].t=d[i]; city[i*2].num=i;
		city[i*2+1].t=(24-d[i])%24; city[i*2+1].num=i;
	}
	qsort(city,n*2,sizeof(City),comp);
	DEBUG("%d\n",check(4));
	left=-1,right=25;
	while(right-left>1){
		mid=(left+right)/2;
		if(check(mid)) left=mid;
		else right=mid;
	}
	printf("%d\n",left);
	return 0;
}