Integer Factorization

#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;
}