#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define FOR(i,a,b) for (int i = (a); i < (b); i++)
using namespace std;
using namespace __gnu_pbds;
using ll=long long;
using ld=long double;
using vi=vector<int>;
template<class T> using oset =tree<T, null_type, less<T>, rb_tree_tag,tree_order_statistics_node_update> ;
//上
const int N = 50001;
int wh[N];
ll inv[5217][5217];
int euclid(int a, int b, ll &x, int &y) {
	if (!b) return x = 1, y = 0, a;
	int d = euclid(b, a % b, y, x);
	return y -= a/b * x, d;
}

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    memset(wh,-1,sizeof(wh));
    vector<int> prime(N+1,1);
    for(int i = 2; i <= N; i++){
        if(prime[i] == 1) for(int j = i; j <=N;j+=i) prime[j] = i;
    }

    vector<pair<int,int>> pot;

    for(int i = 2; i <= N;i++){
        unordered_map<int,int> fac;
        int x = i;
        int r = 1;
        while( x > 1){
            fac[prime[x]]++;
            r *= prime[x];
            x /= prime[x];
            
            if(fac.size() > 1) break;
        }
        if(fac.size() == 1){
            for(auto &u: fac) pot.push_back({u.first,r});
        }
    }
    for(int i = 0; i < 5217;i++) wh[pot[i].second] = i;
    int y;
    for(int i = 0; i < 5217;i++){
        for(int j = 0; j < 5217;j++){
            if(pot[i].first == pot[j].first) continue;
            euclid(pot[j].second,pot[i].second,inv[i][j],y);
            if(inv[i][j] <0) inv[i][j] += pot[i].second;
        }
    }
    int t;
    cin >>t;
    while(t--){
        int n;
        cin >> n;
        if(n == 1){
            cout <<"1/1\n";
            continue;
        }else if(n == 2){
            cout <<"1/2\n";
            continue;
        }
        unordered_map<int,int> mp;
        for(int i = 1; i <= n; i++){
            if(wh[i] != -1){
                mp[pot[wh[i]].first] = wh[i];
            }
        }
        double ans = 0.0;
        int co = 0;
        for(auto &u: mp){
            ll a = 1;
            for(auto &e:mp){
                if(u.first == e.first) continue;
                a =a*inv[u.second][e.second];
                if(a > 1e13) a%= pot[u.second].second;
            }
          a%= pot[u.second].second;
            if(co > 0)cout<<'+';
            cout<<a<<"/"<<pot[u.second].second;
            co++;
            ans += (double)a/(double)pot[u.second].second;
        }
        ans += 0.5;
        cout<<"-"<<floor(ans)<<"/1\n";
    }
}

answer.code: In function ‘int euclid(int, int, ll&, int&)’:
answer.code:17:34: error: cannot bind non-const lvalue reference of type ‘ll&’ {aka ‘long long int&’} to a value of type ‘int’
   17 |         int d = euclid(b, a % b, y, x);
      |                                  ^
answer.code:15:30: note:   initializing argument 3 of ‘int euclid(int, int, ll&, int&)’
   15 | int euclid(int a, int b, ll &x, int &y) {
      |                          ~~~~^