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- #include <bits/stdc++.h>
- using namespace std;
- #define PB push_back
- #define ZERO (1e-10)
- #define INF (1<<30)
- #define CL(A,I) (memset(A,I,sizeof(A)))
- #define DEB printf("DEB!\n");
- #define D(X) cout<<" "<<#X": "<<X<<endl;
- #define EQ(A,B) (A+ZERO>B&&A-ZERO<B)
- typedef long long ll;
- typedef pair<ll,ll> pll;
- typedef vector<int> vi;
- typedef pair<int,int> ii;
- #define IN(n) int n;scanf("%d",&n);
- #define FOR(i, m, n) for (int i(m); i < n; i++)
- #define REP(i, n) FOR(i, 0, n)
- #define F(n) REP(i, n)
- #define FF(n) REP(j, n)
- #define FT(m, n) FOR(k, m, n)
- #define aa first
- #define bb second
- ll R[]={2,3,5,7,11,13,17,19,23,29,31,37},nt(INF);
- ll mm(ll a,ll b,ll M){
- if(a<INF&&b<INF)return (a*b)%M;
- ll v(0),w(a%M);
- while(b)v=b&1?(v+w)%M:v,w=(w<<1)%M,b>>=1;
- return v%M;
- }
- ll pw(ll n,ll k,ll M){
- ll r=1;
- while(k){
- if(k&1)r=mm(r,n,M);
- n=mm(n,n,M),k>>=1;
- }
- return r%M;
- }
- bool isP(ll n){
- if(n<2)return 0;
- if(!(n&1))return n==2;
- ll s=n-1;
- while(!(s&1))s>>=1;
- if(n<40){FT(3,n)if(!(n%k))return 0;return 1;}
- F(12){
- ll z(R[i]),t(s),r(pw(z,t,n));
- if(r==1||!~r==-1)continue;
- while(t!=n-1&&r!=n-1)
- r=mm(r,r,n),t<<=1;
- if(r!=(n-1))return 0;
- }
- return 1;
- }
- ll rnd(int b){
- ll r(0);
- F(b)r<<=1,r|=rand()&1;
- return r;
- }
- ll gcd(ll a,ll b){
- return b?gcd(b,a%b):a;
- }
- ll rho(ll N) {
- if(!(N&1))return 2;
- ll d,c(rnd(ceil(log2(N)-ZERO))),x(rnd(ceil(log2(N)-ZERO))),xx=x;
- do{
- x=mm(x,x,N),x+=c,x%=N;
- xx=mm(xx,xx,N),xx+=c,xx%=N;
- xx=mm(xx,xx,N),xx+=c,xx%=N;
- d=gcd(llabs(x-xx),N);
- }while(d==1);
- return d;
- }
- int ff(ll N,ll*f,int L){
- if(N<=1)return L;
- if(isP(N))return f[L]=N,++L;
- ll d(rho(N));
- return ff(N/d,f,ff(d,f,L));
- }
- int fc(ll N,ll*f,int*c){
- static ll G[66];
- int L(ff(N,G,0)),I(0),l(0);
- G[L]=-1;
- sort(G,G+L);
- while(I<L){
- f[l]=G[I++],c[l]=1;
- while(G[I]==G[I-1])++c[l],++I;
- ++l;
- }
- return l;
- }
- ll N,f[64];
- int h,c[64];
- int main(void){
- while(scanf("%lld",&N),N){
- h=fc(N,f,c);
- F(h){
- if(i)putchar_unlocked(32);
- printf("%lld^%d",f[i],c[i]);
- }
- putchar_unlocked(10);
- }
- return 0;
- }
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