A
G
1 /*1543*/ 2 #include <iostream> 3 #include <string.h> 4 #include <stdio.h> 5 #include <stdlib.h> 6 #include <algorithm> 7 #include <ctime> 8 #include <cmath> 9 #include <set> 10 #define maxn 51000 11 #define LL long long 12 using namespace std; 13 const int Times = 10 ; 14 const int C = 777 ; 15 LL N; 16 LL a[70]; 17 LL b[70]; 18 LL pri[maxn]; 19 LL cnt; 20 set<LL> S; 21 22 LL MIN(LL a,LL b) { return a<b?a:b; } 23 24 LL ABS(LL a) { return a>0?a:-a; } 25 26 LL gcd(LL a,LL b) { return b==0?a:gcd(b,a%b); } 27 28 LL mul_mod(LL a,LL b,LL n) 29 { 30 LL ans=0; 31 while (b>0) 32 { 33 if (b&1) ans+=a; 34 if (ans>n) ans-=n; 35 a<<=1; 36 if (a>n) a-=n; 37 b>>=1; 38 } 39 return ans; 40 } 41 42 LL exp_mod(LL a,LL b,LL n) 43 { 44 LL ans=1; 45 while (b>0) 46 { 47 if (b&1) ans=mul_mod(ans,a,n); 48 a=mul_mod(a,a,n); 49 b>>=1; 50 } 51 return ans; 52 } 53 54 bool miller_rabbin(LL n) 55 { 56 if (n==2) return true; 57 if (n<2 || !(n&1)) return false; 58 int t=0; 59 LL u=n-1,a,x,y; 60 while (!(u&1)) t++,u>>=1; 61 for (int i=0; i<=Times; i++) 62 { 63 a=rand()%(n-1)+1; 64 if (a<0 || a==1) a=n/2; 65 if (exp_mod(a,n-1,n)!=1) return false; 66 x=exp_mod(a,u,n); 67 for (int j=0; j<t; j++) 68 { 69 y=mul_mod(x,x,n); 70 if (y==1 && x!=1 && x!=n-1) return false; 71 x=y; 72 } 73 if (x!=1) return false; 74 } 75 return true; 76 } 77 78 LL pollar_rho(LL n,LL c) 79 { 80 LL d,x,y,i=1,k=2; 81 x=rand()%(n-1)+1; 82 if (x<0) x=-x; 83 y=x; 84 while (1) 85 { 86 i++; 87 x=(mul_mod(x,x,n)+c)%n; 88 d=gcd(ABS(x-y),n); 89 if (d>1 && d<n) return d; 90 if (x==y) return n; 91 if (i==k) 92 y=x,k<<=1; 93 } 94 } 95 96 97 void find(LL n,LL k) 98 { 99 if (n==1) return; 100 if (miller_rabbin(n)) { pri[cnt++]=n; return; } 101 LL p=n; 102 while (p>=n) p=pollar_rho(p,k--); 103 find(p,k); 104 find(n/p,k); 105 } 106 107 void find_max_exp(LL p){ 108 int pos=-1,m=-1; 109 for(int i=0;i<N;i++){ 110 int k=0; 111 LL an=a[i]; 112 while(an%p==0){ 113 k++; 114 an=an/p; 115 } 116 if ((k>m) || (k==m && i>pos)) { 117 pos=i;m=k; 118 } 119 } 120 while(m--){ 121 b[pos]=b[pos]*p; 122 } 123 // cout<<"p="<<p<<","<<"pos="<<pos<<endl; 124 } 125 int main(){ 126 while(cin>>N && N>0){ 127 cnt=0; 128 for(int i=0;i<N;i++){ 129 cin>>a[i]; 130 find(a[i],C); 131 } 132 S.clear(); 133 for(int i=0;i<N;i++) b[i]=1; 134 for(int i=0;i<cnt;i++){ 135 LL p=pri[i]; 136 if (S.count(p)) continue; 137 find_max_exp(p); 138 S.insert(p); 139 } 140 for(int i=0;i<N;i++) if (i==N-1) printf("%lld ",b[i]);else printf("%lld ",b[i]); 141 } 142 return 0; 143 }