#pragma GCC optimize("Ofast")


#include<bits/stdc++.h>
bool Mbg;
using namespace std;
#define vec vector
#define pb push_back
#define eb emplace_back
#define siz(vec) ((int)(vec).size())
#define all(vec) (vec).begin(),(vec).end()
template<class T>
void operator +=(vec<T> &a,T b){a.push_back(b);}
template<class T>
void operator --(vec<T> &a){a.pop_back();}
#define pii pair<int,int>
#define x first
#define y second
#define mp make_pair
#define exc(exp) if(exp)continue;
#define stop(exp) if(exp)break;
#define ret(exp) if(exp)return;
#define deb(var) cerr<<#var<<'='<<(var)<<"; "
#define debl(var) cerr<<#var<<'='<<(var)<<";\n"
#define ins insert
#define era erase
#define lb lower_bound
#define ub upper_bound
#define int long long
#define inf (long long)(1e9)
template<class T>
bool Min(T &x,T y){return x>y?x=y,1:0;}
template<class T>
bool Max(T &x,T y){return x<y?x=y,1:0;}
const int mod=1e9+7;
void Add(int &x,int y){x=x+y<mod?x+y:x+y-mod;}
void Dec(int &x,int y){x=x>=y?x-y:x-y+mod;}
int fpm(int x,int y,int mod){
    int ans=1;for(;y;y>>=1,(x*=x)%=mod)if(y&1)(ans*=x)%=mod;return ans;
}
void exgcd(int a,int b,int &x,int &y){
	if(!b){
        x=1,y=0;
    }else{
        exgcd(b,a%b,y,x);y-=a/b*x;
    }
}
int n;
int phi[50010];
bool nsp[50010];
int tot,prm[50010];
void sieve(){
    for(int i=2;i<=5e4;i++){
        if(!nsp[i]){
            phi[i]=i-1;
            prm[++tot]=i;
        }
        if(i<=10)deb(i),debl(phi[i]);
        for(int j=1;prm[j]*i<=5e4;j++){
            nsp[i*prm[j]]=1;
            if(i%prm[j]==0){
                phi[i*prm[j]]=phi[i]*prm[j];
                break;
            }else{
                phi[i*prm[j]]=phi[i]*(prm[j]-1);
            }
            
        }
    }
}


int c[50010],a[50010],t[50010];

// int rec[7010][7010];
int Inv(int a,int b){
    return fpm(a,phi[b]-1,b);
}
void work(){
    cin>>n;
    if(n==1){
        cout<<"1/1\n";
        return;
    }

    vec<int> ps;
    for(int i=2;i<=n;i++){
        exc(nsp[i]);
        ps+=i;

        c[i]=0,a[i]=1;
        while(a[i]*i<=n){
            a[i]*=i,++c[i];
        }
    }

    
    for(int i=2;i<=n;i++){
        exc(nsp[i]);
        
        int M=1,T=0;
        for(auto j:ps){
            stop(j>=i);
            M=M*a[j];
            if(((T++)&3)==3){
                M=M%a[i];
            }
        }
        M=M%a[i];


        int x,y;
        exgcd(a[i],M,y,x);

        t[i]=x%a[i];

        for(auto j:ps){
            stop(j>=i);

            (t[j]*=y+M*x*Inv(a[i],a[j]))%=a[j];
        }
    }

    long double ext=0;
    for(int i=1;i<=n;i++){
        exc(nsp[i]||!t[i]);
        ext+=(long double)t[i]/a[i];
    }


    int x=-floor(ext+0.3);
    
    bool fir=1;
    if(x!=0){
        cout<<x<<"/1";
        fir=0;
    }
    
    for(int i=2;i<=n;i++){
        exc(nsp[i]||t[i]==0);
        if(!fir&&t[i]>0)cout<<'+';
        fir=0;
        cout<<t[i]<<'/'<<a[i];
    }
    cout<<'\n';
}
bool Med;
signed main(){
    sieve();
    ios::sync_with_stdio(0),
    cin.tie(0),cout.tie(0);
    int T=1;cin>>T;while(T--)work();
    // cerr<<"Time: "<<clock()<<" ms;\n";
    // cerr<<"Memory: "<<abs(&Med-&Mbg)/1024.0/1024.0<<" MiB.\n";
}
/*
- CONTINUE, NON-STOPPING, FOR THE FAITH
- START TYPING IF YOU DON'T KNOW WHAT TO DO
- STOP TYPING IF YOU DON'T KNOW WHAT YOU'RE DOING
*/