Problem:
Score : 300 points

Problem Statement

There are N monsters, numbered 1, 2, ..., N.

Initially, the health of Monster i is A_i.

Below, a monster with at least 1 health is called alive.

Until there is only one alive monster, the following is repeated:

A random alive monster attacks another random alive monster.

As a result, the health of the monster attacked is reduced by the amount equal to the current health of the monster attacking.

Find the minimum possible final health of the last monster alive.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

1 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the minimum possible final health of the last monster alive.

Sample Input 1

4
2 10 8 40

Sample Output 1

2

When only the first monster keeps on attacking, the final health of the last monster will be 2, which is minimum.

Sample Input 2

4
5 13 8 1000000000

Sample Output 2

1

Sample Input 3

3
1000000000 1000000000 1000000000

Sample Output 3

1000000000

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#pragma GCC optimize("Ofast")
#include<bits/stdc++.h>
using namespace::std;
//struct __INIT{__INIT(){cin.tie(0);ios::sync_with_stdio(false);cout<<fixed<<setprecision(15);}} __init;
__attribute__((constructor))
void init(){
	cin.tie(0);
	ios::sync_with_stdio(false);
	cout<<fixed<<setprecision(15);
}
// random_device rd;
// mt19937 mt(rd());
// #include <boost/numeric/interval.hpp>
// #include <boost/numeric/interval/io.hpp>
// #include <boost/intrusive/rbtree.hpp>
// #include <boost/dynamic_bitset.hpp>
// #include <boost/geometry.hpp>
// #include <boost/geometry/geometries/linestring.hpp>
// #include <boost/geometry/geometries/polygon.hpp>
// #include <boost/geometry/geometries/point_xy.hpp>
// #include <boost/math/tools/minima.hpp>
// using boost::math::tools::brent_find_minima;
// #include <boost/multiprecision/cpp_dec_float.hpp>
// #include <boost/multiprecision/cpp_int.hpp>
// namespace mp = boost::multiprecision;
// typedef mp::number<mp::cpp_dec_float<256>> cdouble;
// typedef mp::cpp_int cint;

#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/priority_queue.hpp>
#include<ext/pb_ds/tag_and_trait.hpp>
template<typename T=long long>using pbds=__gnu_pbds::tree<T,__gnu_pbds::null_type,less<T>,__gnu_pbds::rb_tree_tag,__gnu_pbds::tree_order_statistics_node_update>;
template<typename T=long long>using pbds_map=__gnu_pbds::tree<T,T,less<T>,__gnu_pbds::rb_tree_tag,__gnu_pbds::tree_order_statistics_node_update>;
template<typename T=long long>using pqueue =__gnu_pbds::priority_queue<T, less<T>,__gnu_pbds::rc_binomial_heap_tag>;
typedef long long lint;
typedef long long ll;
typedef long double ldouble;
typedef vector<lint> vec;
typedef vector<vector<lint>> mat;
typedef vector<vector<vector<lint>>> mat3;
typedef vector<double> dvec;
typedef vector<vector<double>> dmat;
typedef vector<vector<vector<double>>> dmat3;
typedef vector<string> svec;
typedef vector<vector<string>> smat;
typedef vector<vector<vector<string>>> smat3;
typedef vector<pair<lint,lint>> pvec;
typedef vector<vector<pair<lint,lint>>> pmat;
typedef vector<vector<vector<pair<lint,lint>>>> pmat3;
#define rep(i, n) for(lint i = 0; i < (lint)(n); i++)
#define irep(i) for(lint i = 0;; i++)
#define irep1(i) for(lint i = 1;; i++)
#define irep2(i) for(lint i = 2;; i++)
#define rrep(i, n) for(lint i = (lint)(n-1); i >-1; i--)
#define rrepi(i,a,b) for(lint i = (lint)(b-1); i >a-1; i--)
#define repi(i,a,b) for(lint i=lint(a);i<lint(b);i++)
#define rep2(i,a,b,c) for(lint i=lint(a);i>lint(b);i+=c)
#define all(x) (x).begin(),(x).end()
#define PI 3.141592653589793
#define dist(x1,y1,x2,y2) (pow(pow(x2-x1,2)+pow(y2-y1,2),0.5))
#define input(a,n) lint n;cin>>n;vector<lint>a(n);rep(i,n)cin>>a[i];
#define SUM(v) accumulate(all(v),0LL)
#define INF (1LL<<60)
#define IINF (1<<30)
#define EPS (1e-10)
#define LINF 9223372036854775807
//#define MOD 998244353LL
#define MOD 1000000007LL
#define endl "\n"
template<typename T>inline void numout(T t){bool f=0;for(auto i:t){cout<<(f?" ":"")<<i<INF/2?i:"INF";f=1;}cout<<endl;}
template<typename T>inline void numout2(T t){for(auto i:t)numout(i);}
template<typename T>inline void output(T t){bool f=0;for(auto i:t){cout<<(f?" ":"")<<i;f=1;}cout<<endl;}
template<typename T>inline void output2(T t){for(auto i:t)output(i);}
template<typename T>inline void _output(T t){bool f=0;for(int i=0;i<t.size();i++){cout<<f?"":" "<<t[i];f=1;}cout<<endl;}
template<typename T>inline void _output2(T t){for(int i=0;i<t.size();i++)output(t[i]);}
auto Y=[&](auto f){return[&](auto... args){return f(f, args...);};};
template<typename T=lint>T in(){return *istream_iterator<T>(cin);}
template<typename T=lint>inline T gcd(T a,T b){return b?gcd(b,a%b):a;}
template<typename T=lint>inline T lcm(T a,T b){return a/gcd(a,b)*b;}
template<typename T=lint>inline T minq(T a,T b){return min(a,b);}
inline bool chmin(auto& s,const auto& t){bool res=s>t;s=min(s,t);return res;}
inline bool chmax(auto& s,const auto& t){bool res=s<t;s=max(s,t);return res;}
vector<int> dx={-1,1,0,0,1,1,-1,-1};
vector<int> dy={0,0,-1,1,1,-1,1,-1};

class FFT{
	using lint=long long;
	using C=complex<double>;
	lint n=1;
    public:
	vector<lint> mul(vector<lint> a,vector<lint> b){
		int size=a.size()+b.size()-1;
		while(n<size)n<<=1;
		auto ac=itoc(a,n);
		auto bc=itoc(b,n);
		auto ia=fft(ac,false);
		auto ib=fft(bc,false);
		vector<C> ires(n);
		for(int i=0;i<n;i++)ires[i]=ia[i]*ib[i];
		auto res=ctoi(fft(ires,true),size);
		return res;
	}
	private:
	vector<C> itoc(vector<lint> v,int size){
		vector<C> res(size);
		for(int i=0;i<min<int>(size,v.size());i++)res[i]=v[i];
		return res;
	}
	vector<lint> ctoi(vector<C> v,int size){
		vector<lint> res(size);
		for(int i=0;i<min<int>(size,v.size());i++)res[i]=round(v[i].real()/n);
		return res;
	}
	vector<C> fft(vector<C> v,bool inv){
		int n=v.size();
		assert((n&(n-1))==0);
		if(n==1)return v;
		vector<C> v1(n/2);
		vector<C> v2(n/2);
		for(int i=0;i<n/2;i++)v1[i]=v[i*2];
		for(int i=0;i<n/2;i++)v2[i]=v[i*2+1];
		auto iv1=fft(v1,inv);
		auto iv2=fft(v2,inv);
		vector<C> res(n);
		C zeta;
		for(int i=0;i<n;i++){
			if(inv)zeta=C(cos(2*M_PI*i/n),-sin(2*M_PI*i/n));
			else zeta=C(cos(2*M_PI*i/n),sin(2*M_PI*i/n));
			res[i]=iv1[i%(n/2)]+zeta*iv2[i%(n/2)];
		}
		return res;
	}
};

int main(){
    lint n;
    cin>>n;
    vec a(n);
    rep(i,n)cin>>a[i];
    lint ans=0;
    rep(i,n){
        ans=gcd(ans,a[i]);
    }
    cout<<ans<<endl;
}