Problem:
Score: 200 points

Problem Statement

You are an immigration officer in the Kingdom of AtCoder. The document carried by an immigrant has some number of integers written on it, and you need to check whether they meet certain criteria.

According to the regulation, the immigrant should be allowed entry to the kingdom if and only if the following condition is satisfied:

All even numbers written on the document are divisible by 3 or 5.

If the immigrant should be allowed entry according to the regulation, output APPROVED; otherwise, print DENIED.

Notes

The condition in the statement can be rephrased as "If x is an even number written on the document, x is divisible by 3 or 5".
Here "if" and "or" are logical terms.

Constraints

All values in input are integers.

1 \leq N \leq 100

1 \leq A_i \leq 1000

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \dots A_N

Output

If the immigrant should be allowed entry according to the regulation, print APPROVED; otherwise, print DENIED.

Sample Input 1

5
6 7 9 10 31

Sample Output 1

APPROVED

The even numbers written on the document are 6 and 10.

All of them are divisible by 3 or 5, so the immigrant should be allowed entry.

Sample Input 2

3
28 27 24

Sample Output 2

DENIED

28 violates the condition, so the immigrant should not be allowed entry.

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

#include<bits/stdc++.h>
using namespace std;
#define int long long
#define double long double
#define fo(a,b) for(int a=0;a<b;a++)
#define Sort(a) sort(a.begin(),a.end())
#define rev(a) reverse(a.begin(),a.end())
#define fi first
#define se second
#define sz size()
#define bgn begin()
#define en end()
#define pb push_back
#define pp() pop_back()
#define V vector
#define P pair
#define yuko(a) setprecision(a)
#define uni(a) a.erase(unique(a.begin(),a.end()),a.end())
#define Q queue
#define pri priority_queue
#define Pri priority_queue<int,vector<int>,greater<int>>
#define PriP priority_queue<P<int,int>,vector<P<int,int>>,greater<P<int,int>>>
#define ff first.first
#define fs first.second
#define sf second.first
#define ss second.second
#define all(a)  (a).begin(),(a).end()
#define elif else if
int low(V<int> a,int b){
  decltype(a)::iterator c=lower_bound(a.begin(),a.end(),b);
  int d=c-a.bgn;
  return d;
}
int upp(V<int> a,int b){
  decltype(a)::iterator c=upper_bound(a.begin(),a.end(),b);
  int d=c-a.bgn;
  return d;
}
template<class T>
 void cou(vector<vector<T>> a){
  int b=a.size();
  int c=a[0].size();
  fo(i,b){
    fo(j,c){
      cout<<a[i][j];
      if(j==c-1)
        cout<<endl;
      else
        cout<<' ';
    }
  }
}
int wari(int a,int b) {
  if(a%b==0)
    return a/b;
  else
    return a/b+1;
}
int keta(int a){
  double b=a;
  b=log10(b);
  int c=b;
  return c+1;
}
int souwa(int a){
  return a*(a+1)/2;
}
int gcm(int a,int b){
  if(a%b==0)
    return b;
  return gcm(b,a%b);
}
bool prime(int a){
  if(a<2)
    return false;
  else if(a==2)
    return true;
  else if(a%2==0)
    return false;
  for(int i=3;i<=sqrt(a)+1;i+=2){
    if (a%i==0)
      return false;
  }
  return true;
}
struct Union{
  vector<int> par;
  Union(int a){
  par=vector<int>(a,-1);
  }
  int find(int a){
    if(par[a]<0)
      return a;
    else
      return par[a]=find(par[a]);
  }
  bool same(int a,int b){
    return find(a)==find(b);
  }
  int Size(int a){
    return -par[find(a)];
  }
  void unite(int a,int b){
    a=find(a);
    b=find(b);
    if(a==b)
      return;
    if(Size(b)>Size(a))
      swap<int>(a,b);
    par[a]+=par[b];
    par[b]=a;
  }
};
int ketas(int a){
  string b=to_string(a);
  int c=0;
  fo(i,keta(a)){
    c+=b[i]-'0';
  }
  return c;
}
bool fe(int a,int b){
  a%=10;
  b%=10;
  if(a==0)
    a=10;
  if(b==0)
    b=10;
  if(a>b)
    return true;
  else
    return false;
}
int INF=1000000007;
struct edge{int s,t,d; };
V<int> mojisyu(string a){
  V<int> b(26,0);
  fo(i,a.sz){
    b[a[i]-'a']++;
  }
  return b;
}
int wa2(int a){
  if(a%2==1)
    return a/2;
  return a/2-1;
}
/*signed main(){
  int a,b,c;
  cin>>a>>b>>c;
  V<V<edge>> d(a);
  fo(i,b){
    edge e;
    cin>>e.s>>e.t>>e.d;
    d[e.s].pb(e);
  }
  V<int> e(a,INF);
  e[c]=0;
  priority_queue<P<int,int>,V<P<int,int>>,greater<P<int,int>>> f;
  f.push({0,c});
  int h=INF;
  while(!f.empty()){
    P<int,int> g;
    g=f.top();
    f.pop();
    int v = g.second, i = g.first;
    for(edge l : d[v]){
      if(e[l.t] > i + l.d){
        e[l.t] = i + l.d;
        f.push({i+l.d , l.t});
      }
    }
  }
  fo(i,a){
    if(e[i]==INF)
      cout<<"INF"<<endl;
    else
      cout<<e[i]<<endl;
  }
}
?*/
int nCr(int n,int r){
  int a=1;
  r=min(r,n-r);
  for(int i=n;i>n-r;i--){
    a*=i;
    a/=n-i+1;
  }
  return a;
}
/*void sea(int x,int y){
  if(x<0||a<=x||y<0||b<=y||c[x][y]=='#')
    return;
  if(d[x][y])
    return;
  d[x][y]++;
  sea(x+1,y);
  sea(x-1,y);
  sea(x,y+1);
  sea(x,y-1);
}*/
int kaijou(int a){
  int b=1;
  fo(i,a)
    b*=i+1;
  return b;
}
int nPr(int a,int b){
  if(a<b)
    return 0;
  if(b==0)
    return 1;
  int c=1;
  for(int i=a;i>a-b;i--){
    c*=i;
    c%=INF;
  }
  return c;
}
int modinv(int a,int m){
  int b=m,u=1,v=0;
  while(b){
    int t=a/b;
    a-=t*b;
    swap(a,b);
    u-=t*v;
    swap(u,v);
  }
  u%=m;
  if(u<0)
    u+=m;
  return u;
}
int lcm(int a,int b){
  int c=modinv(gcm(a,b),INF);
  return ((a*c)%INF)*(b%INF)%INF;
}
int MOD=INF;
int fac[1000010], finv[1000010], inv[1000010]; 
// テーブルを作る前処理
//先にCOMinit()で前処理をする
//ABC145D
void COMinit() {
  fac[0]=fac[1]=1;
  finv[0]=finv[1]=1;
  inv[1]=1;
  for(int i=2;i<1000010;i++){
    fac[i]=fac[i-1]*i%MOD;
    inv[i]=MOD-inv[MOD%i]*(MOD/i)%MOD;
    finv[i]=finv[i-1]*inv[i]%MOD;
  }
}
// 二項係数計算
int COM(int n,int k){
  if(n<k)
    return 0;
  if(n<0||k<0)
    return 0;
  return fac[n]*(finv[k]*finv[n-k]%MOD)%MOD;
}
bool naka(int a,int b,V<V<char>> c){
  return (a>=0&&b>=0&&a<c.sz&&b<c[0].sz);
}

V<P<int,int>> mawari8={{0,-1},{0,1},{1,0},{-1,0},{-1,-1},{1,1},{1,-1},{-1,-1}};
int inf=1000000000000000007;
/*
signed main(){
  int a,b,c;
  cin>>a>>b>>c;
  V<V<edge>> d(a);
  fo(i,b){
    edge e;
    cin>>e.s>>e.t>>e.d;
    d[e.s].pb(e);
  }
  V<int> e(a,INF);
  e[c]=0;
  priority_queue<P<int,int>,V<P<int,int>>,greater<P<int,int>>> f;
  f.push({0,c});
  int h=INF;
  while(!f.empty()){
    P<int,int> g;
    g=f.top();
    f.pop();
    int v = g.second, i = g.first;
    for(edge l : d[v]){
      if(e[l.t] > i + l.d){
        e[l.t] = i + l.d;
        f.push({i+l.d , l.t});
      }
    }
  }
  fo(i,a){
    if(e[i]==INF)
      cout<<"INF"<<endl;
    else
      cout<<e[i]<<endl;
  }
}*/
V<P<int,int>> mawari4={{0,-1},{0,1},{1,0},{-1,0}};
//最短経路の表 a(全部INFで初期化)
//縦横 x,y
//迷路 f
//スタートsx,sy
//ゴールgx,gy
//文字はgから使おうね
/*int bfs_haba(){
  Q<P<int,int>> b;
  a[sx][sy]=0;
  b.push({sx,sy});
  while(!b.empty()){
    P<int,int> c=b.front();
    b.pop();
    if(c.fi==gx&&c.se==gy){
      break;
    }
    fo(i,4){
      int d=c.fi+mawari4[i].fi;
      int e=c.se+mawari4[i].se;
      if(0<=d&&0<=e&&d<x&&e<y&&f[d][e]!='#'&&a[d][e]==INF){
        b.push({d,e});
        a[d][e]=1+a[c.fi][c.se];
      }
    }
  }
  return a[gx][gy];
}*/
V<int> onajibubun(string a){
  V<int> b(a.sz);
  for(int i=1,j=0;i<a.sz;i++){
    if(i+b[i-j]<j+b[j])
      b[i]=b[i-j];
    else{
      int c=max<int>(0,j+b[j]-i);
      while(i+c<a.sz&&a[c]==a[i+c])
        c++;
      b[i]=c;
      j=i;
    }
  }
  b[0]=a.sz;
  return b;
}
//各頂点ごとにどこに辺が出てるかの表がc
//各頂点ごとの色を表すV<int>(頂点数max)のcolorを用意する
//aはどこ塗るか、bは何で塗るかなので、(0,1,c)でよぶとおけ
V<int> color(205);
bool nibu_hantei(int a,int b,V<V<int>> c){
  color[a]=b;
  fo(i,c[a].sz){
    if(b==color[c[a][i]])
      return false;
    if(color[c[a][i]]==0&&!nibu_hantei(c[a][i],-b,c))
      return false;
  }
  return true;
}
//aは頂点数
//nibu_hanteiの上にcolorを用意する
//各頂点ごとにどこに辺が出てるかの表がc
bool renketujanai_nibu_hantei(int a,V<V<int>> c){
  fo(i,a){
    if(color[i]==0){
      if(!nibu_hantei(i,1,c))
        return false;
    }
  }
  return true;
}
signed main(){
  int n;
  cin>>n;
  int b=1;
  V<int> a(n);
  fo(i,n){
    cin>>a[i];
  }
  fo(i,n){
    if(a[i]%2==0){
      if(a[i]%3==0&&a[i]%5==0)
        b=1;
      else
        b=0;
    }

  }
  if(b)
    cout<<"APPROVED"<<endl;
  else
    cout<<"DENIED"<<endl;
}