Problem p03810 (C++)

Buggy submission (status: Runtime Error):
/*

                   _ooOoo_
                  o8888888o
                  88" . "88
                  (| -_- |)
                  O\  =  /O
               ____/`---'\____
             .'  \\|     |//  `.
            /  \\|||  :  |||//  \
           /  _||||| -:- |||||-  \
           |   | \\\  -  /// |   |
           | \_|  ''\---/''  |   |
           \  .-\__  `-`  ___/-. /
         ___`. .'  /--.--\  `. . __
      ."" '<  `.___\_<|>_/___.'  >'"".
     | | :  `- \`.;`\ _ /`;.`/ - ` : | |
     \  \ `-.   \_ __\ /__ _/   .-` /  /
======`-.____`-.___\_____/___.-`____.-'======
                   `=---='
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                    prayer
*/

// g++ -std=c++11 a.cpp
#include <algorithm>
#include <assert.h>
#include <bitset>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <typeinfo>
#include <unordered_map>
#include <utility>
#include <vector>
#define loop(i, a, b) for (int i = a; i < b; i++)
#define rep(i, a) loop(i, 0, a)
#define FOR(i, a) for (auto i : a)
#define pb push_back
#define all(in) in.begin(), in.end()
#define shosu(x) fixed << setprecision(x)
#define show1d(v)                                                              \
  rep(i, v.size()) cout << " " << v[i];                                        \
  cout << endl << endl;
#define show2d(v)                                                              \
  rep(i, v.size()) {                                                           \
    rep(j, v[i].size()) cout << " " << v[i][j];                                \
    cout << endl;                                                              \
  }                                                                            \
  cout << endl;
using namespace std;
// kaewasuretyuui
typedef long long ll;
#define int ll
typedef int Def;
typedef pair<Def, Def> pii;
typedef vector<Def> vi;
typedef vector<vi> vvi;
typedef vector<pii> vp;
typedef vector<vp> vvp;
typedef vector<string> vs;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef pair<Def, pii> pip;
typedef vector<pip> vip;
// #define mt make_tuple
// typedef tuple<int,int,int> tp;
// typedef vector<tp> vt;
template <typename A, typename B> bool cmin(A &a, const B &b) {
  return a > b ? (a = b, true) : false;
}
template <typename A, typename B> bool cmax(A &a, const B &b) {
  return a < b ? (a = b, true) : false;
}
// template<class C>constexpr int size(const C &c){return (int)c.size();}
// template<class T,size_t N> constexpr int size(const T
// (&xs)[N])noexcept{return (int)N;}
const double PI = acos(-1);
const double EPS = 1e-9;
Def inf = sizeof(Def) == sizeof(long long) ? 2e18 : 1e9 + 10;
int dx[] = {0, 1, 0, -1};
int dy[] = {1, 0, -1, 0};
int gcd(int a, int b) { return b ? gcd(b, a % b) : a; }
signed main() {
  int n;
  cin >> n;
  vi in(n);
  rep(i, n) cin >> in[i];
  int h = 0;
  while (1) {
    int co = 0, g = 0;
    int ma = 1;
    rep(i, n) if (in[i] - 1) {
      if (in[i] % 2)
        cmax(ma, in[i]);
      co += in[i] % 2 == 0, in[i] -= in[i] % 2, g = gcd(g, in[i]);
    }
    rep(i, n) in[i] /= g;
    if (co % 2) {
      if (h)
        cout << "Second" << endl;
      else
        cout << "First" << endl;
      return 0;
    } else {
      if (n - co - 1 || ma == 1) {
        if (!h)
          cout << "Second" << endl;
        else
          cout << "First" << endl;
        return 0;
      }
    }
    h ^= 1;
  }
}


Fixed submission:
/*

                   _ooOoo_
                  o8888888o
                  88" . "88
                  (| -_- |)
                  O\  =  /O
               ____/`---'\____
             .'  \\|     |//  `.
            /  \\|||  :  |||//  \
           /  _||||| -:- |||||-  \
           |   | \\\  -  /// |   |
           | \_|  ''\---/''  |   |
           \  .-\__  `-`  ___/-. /
         ___`. .'  /--.--\  `. . __
      ."" '<  `.___\_<|>_/___.'  >'"".
     | | :  `- \`.;`\ _ /`;.`/ - ` : | |
     \  \ `-.   \_ __\ /__ _/   .-` /  /
======`-.____`-.___\_____/___.-`____.-'======
                   `=---='
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
                    prayer
*/

// g++ -std=c++11 a.cpp
#include <algorithm>
#include <assert.h>
#include <bitset>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <typeinfo>
#include <unordered_map>
#include <utility>
#include <vector>
#define loop(i, a, b) for (int i = a; i < b; i++)
#define rep(i, a) loop(i, 0, a)
#define FOR(i, a) for (auto i : a)
#define pb push_back
#define all(in) in.begin(), in.end()
#define shosu(x) fixed << setprecision(x)
#define show1d(v)                                                              \
  rep(i, v.size()) cout << " " << v[i];                                        \
  cout << endl << endl;
#define show2d(v)                                                              \
  rep(i, v.size()) {                                                           \
    rep(j, v[i].size()) cout << " " << v[i][j];                                \
    cout << endl;                                                              \
  }                                                                            \
  cout << endl;
using namespace std;
// kaewasuretyuui
typedef long long ll;
#define int ll
typedef int Def;
typedef pair<Def, Def> pii;
typedef vector<Def> vi;
typedef vector<vi> vvi;
typedef vector<pii> vp;
typedef vector<vp> vvp;
typedef vector<string> vs;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef pair<Def, pii> pip;
typedef vector<pip> vip;
// #define mt make_tuple
// typedef tuple<int,int,int> tp;
// typedef vector<tp> vt;
template <typename A, typename B> bool cmin(A &a, const B &b) {
  return a > b ? (a = b, true) : false;
}
template <typename A, typename B> bool cmax(A &a, const B &b) {
  return a < b ? (a = b, true) : false;
}
// template<class C>constexpr int size(const C &c){return (int)c.size();}
// template<class T,size_t N> constexpr int size(const T
// (&xs)[N])noexcept{return (int)N;}
const double PI = acos(-1);
const double EPS = 1e-9;
Def inf = sizeof(Def) == sizeof(long long) ? 2e18 : 1e9 + 10;
int dx[] = {0, 1, 0, -1};
int dy[] = {1, 0, -1, 0};
int gcd(int a, int b) { return b ? gcd(b, a % b) : a; }
signed main() {
  int n;
  cin >> n;
  vi in(n);
  rep(i, n) cin >> in[i];
  int h = 0;
  while (1) {
    int co = 0, g = 0;
    int ma = 1;
    rep(i, n) if (in[i] - 1) {
      if (in[i] % 2)
        cmax(ma, in[i]);
      co += in[i] % 2 == 0, in[i] -= in[i] % 2, g = gcd(g, in[i]);
    }
    if (g)
      rep(i, n) in[i] /= g;
    if (co % 2) {
      if (h)
        cout << "Second" << endl;
      else
        cout << "First" << endl;
      return 0;
    } else {
      if (n - co - 1 || ma == 1) {
        if (!h)
          cout << "Second" << endl;
        else
          cout << "First" << endl;
        return 0;
      }
    }
    h ^= 1;
  }
}