//#ifdef NACHIA
//#define _GLIBCXX_DEBUG
//#else
//#define NDEBUG
//#endif
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(int i=0; i<int(n); i++)
const i64 INF = 1001001001001001001;
template<typename A> void chmin(A& l, const A& r){ if(r < l) l = r; }
template<typename A> void chmax(A& l, const A& r){ if(l < r) l = r; }
using namespace std;
#include <array>

#include <cassert>


namespace nachia{

namespace prime_sieve_explicit_internal{
    std::vector<bool> isprime = { false }; // a[x] := isprime(2x+1)

    void CalcIsPrime(int z){
        if((int)isprime.size() *2+1 < z+1){
            int new_z = isprime.size();
            while(new_z*2+1 < z+1) new_z *= 2;
            z = new_z-1;
            isprime.resize(z+1, true);
            for(int i=1; i*(i+1)*2<=z; i++) if(isprime[i]){
                for(int j=i*(i+1)*2; j<=z; j+=i*2+1) isprime[j] = false;
            }
        }
    }
    
    std::vector<int> prime_list = {2};
    int prime_list_max = 0;

    void CalcPrimeList(int z){
        while((int)prime_list.size() < z){
            if((int)isprime.size() <= prime_list_max + 1) CalcIsPrime(prime_list_max * 2 + 10);
            for(int p=prime_list_max+1; p<(int)isprime.size(); p++){
                if(isprime[p]) prime_list.push_back(p*2+1);
            }
            prime_list_max = isprime.size() - 1;
        }
    }

    void CalcPrimeListUntil(int z){
        if(prime_list_max < z){
            CalcIsPrime(z);
            for(int p=prime_list_max+1; p<(int)isprime.size(); p++){
                if(isprime[p]) prime_list.push_back(p*2+1);
            }
            prime_list_max = isprime.size() - 1;
        }
    }

}


bool IsprimeExplicit(int n){
    using namespace prime_sieve_explicit_internal;
    if(n == 2) return true;
    if(n % 2 == 0) return false;
    CalcIsPrime(n);
    return isprime[(n-1)/2];
}

int NthPrimeExplicit(int n){
    using namespace prime_sieve_explicit_internal;
    CalcPrimeList(n);
    return prime_list[n];
}

int PrimeCountingExplicit(int n){
    using namespace prime_sieve_explicit_internal;
    if(n < 2) return 0;
    CalcPrimeListUntil(n);
    auto res = std::upper_bound(prime_list.begin(), prime_list.end(), n) - prime_list.begin();
    return (int)res;
}

// [l, r)
std::vector<bool> SegmentedSieveExplicit(long long l, long long r){
    assert(0 <= l); assert(l <= r);
    long long d = r - l;
    if(d == 0) return {};
    std::vector<bool> res(d, true);
    for(long long p=2; p*p<=r; p++) if(IsprimeExplicit(p)){
        long long il = (l+p-1)/p, ir = (r+p-1)/p;
        if(il <= p) il = p;
        for(long long i=il; i<ir; i++) res[i*p-l] = false;
    }
    if(l < 2) for(long long p=l; p<2 && p<r; p++) res[l-p] = false;
    return res;
}


} // namespace nachia

#include <utility>
namespace nachia{

// ax + by = gcd(a,b)
// return ( x, - )
std::pair<long long, long long> ExtGcd(long long a, long long b){
    long long x = 1, y = 0;
    while(b){
        long long u = a / b;
        std::swap(a-=b*u, b);
        std::swap(x-=y*u, y);
    }
    return std::make_pair(x, a);
}

} // namespace nachia

namespace nachia{

class DynamicModSupplier{
    using u64 = unsigned long long;
    using Int = unsigned int;
private:
    u64 imod;
    Int mod;
    // atcoder library
    u64 reduce2(u64 z) const noexcept {
        // atcoder library
#ifdef _MSC_VER
        u64 x; _umul128(z, im, &x);
#else
        using u128 = unsigned __int128;
        u64 x = (u64)(((u128)(z)*imod) >> 64);
#endif
        return z - x * mod;
    }
public:
    DynamicModSupplier(unsigned int MOD = 998244353) : mod(MOD) {
        assert(2 <= MOD);
        assert(MOD < (1u << 31));
        imod = (u64)(-1) / mod + 1;
    }
    Int reduce(u64 z) const noexcept {
        Int v = reduce2(z);
        if(mod <= v) v += mod;
        return v;
    }
    Int add(Int a, Int b) const { a += b; if(a >= mod){ a -= mod; } return a; }
    Int sub(Int a, Int b) const { a -= b; if(a >= mod){ a += mod; } return a; }
    Int mul(Int a, Int b) const { return reduce((u64)a * b); }
    Int muladd(Int a, Int b, Int c) const { return reduce((u64)a * b + c); }
    Int inv(Int a) const {
        Int v = ExtGcd(a, mod).first;
        return (v < mod) ? v : (v + mod);
    }
    Int pow(Int a, u64 i) const {
        Int r = a, ans = 1;
        while(i){
            if(i & 1) ans = mul(ans, r);
            i /= 2;
            r = mul(r, r);
        }
        return ans;
    }
    Int getMod() const { return mod; }
};

} // namespace nachia

namespace nachia{

template<unsigned int IDENTIFER, class IDENTIFER2 = void>
class DynamicModint{
    using Int = unsigned int;
    using MyType = DynamicModint;
private:
    static DynamicModSupplier _c;
    Int v;
    template< class Elem >
    static Elem SafeMod(Elem x, Int mod){
        if(x < 0){
            if(0 <= x+mod) return x + mod;
            return mod - ((-(x+mod)-1) % mod + 1);
        }
        return x % mod;
    }
public:
    DynamicModint() : v(0) {}
    DynamicModint(const MyType& r) : v(r.v) {}
    MyType& operator=(const MyType&) = default;
    DynamicModint(long long x){ v = SafeMod(x, _c.getMod()); }
    static MyType raw(Int _v){ MyType res; res.v = _v; return res; }
    static void setMod(DynamicModSupplier sup){ _c = std::move(sup); }
    MyType operator+=(MyType r){ return v = _c.add(v, r.v); }
    MyType operator+(MyType r) const { return raw(_c.add(v, r.v)); }
    MyType operator-=(MyType r){ return v = _c.sub(v, r.v); }
    MyType operator-(MyType r) const { return raw(_c.sub(v, r.v)); }
    MyType operator-() const { return raw(v ? _c.getMod()-v : 0); }
    MyType operator*=(MyType r){ return v = _c.mul(v, r.v); }
    MyType operator*(MyType r) const { return raw(_c.mul(v, r.v)); }
    MyType operator/=(MyType r){ return v = _c.mul(v, _c.inv(r.v)); }
    MyType operator/(MyType r) const { return raw(_c.mul(v, _c.inv(r.v))); }
    MyType inv() const { return raw(_c.inv(v)); }
    MyType pow(unsigned long long r) const { return raw(_c.pow(v, r)); }
    MyType mulAdd(MyType mul, MyType add) const { return raw(_c.muladd(v, mul.v, add.v)); }
    Int val() const { return v; }
    Int operator*() const { return v; }
    static Int mod(){ return _c.getMod(); }
};

template<unsigned int IDENTIFER, class IDENTIFER2>
DynamicModSupplier DynamicModint<IDENTIFER, IDENTIFER2>::_c;

} // namespace nachia

namespace nachia{

template<unsigned int MOD>
struct StaticModint{
private:
    using u64 = unsigned long long;
    unsigned int x;
public:

    using my_type = StaticModint;
    template< class Elem >
    static Elem safe_mod(Elem x){
        if(x < 0){
            if(0 <= x+MOD) return x + MOD;
            return MOD - ((-(x+MOD)-1) % MOD + 1);
        }
        return x % MOD;
    }

    StaticModint() : x(0){}
    StaticModint(const my_type& a) : x(a.x){}
    StaticModint& operator=(const my_type&) = default;
    template< class Elem >
    StaticModint(Elem v) : x(safe_mod(v)){}
    unsigned int operator*() const noexcept { return x; }
    my_type& operator+=(const my_type& r) noexcept { auto t = x + r.x; if(t >= MOD) t -= MOD; x = t; return *this; }
    my_type operator+(const my_type& r) const noexcept { my_type res = *this; return res += r; }
    my_type& operator-=(const my_type& r) noexcept { auto t = x + MOD - r.x; if(t >= MOD) t -= MOD; x = t; return *this; }
    my_type operator-(const my_type& r) const noexcept { my_type res = *this; return res -= r; }
    my_type operator-() const noexcept { my_type res = *this; res.x = ((res.x == 0) ? 0 : (MOD - res.x)); return res; }
    my_type& operator*=(const my_type& r)noexcept { x = (u64)x * r.x % MOD; return *this; }
    my_type operator*(const my_type& r) const noexcept { my_type res = *this; return res *= r; }
    my_type pow(unsigned long long i) const noexcept {
        my_type a = *this, res = 1;
        while(i){ if(i & 1){ res *= a; } a *= a; i >>= 1; }
        return res;
    }
    my_type inv() const { return my_type(ExtGcd(x, MOD).first); }
    unsigned int val() const noexcept { return x; }
    static constexpr unsigned int mod() { return MOD; }
    static my_type raw(unsigned int val) noexcept { auto res = my_type(); res.x = val; return res; }
    my_type& operator/=(const my_type& r){ return operator*=(r.inv()); }
    my_type operator/(const my_type& r) const { return operator*(r.inv()); }
};

} // namespace nachia

i64 powm(i64 a, i64 i, i64 m){
    if(i == 0) return 1 % m;
    auto x = powm(a*a%m, i/2, m);
    if(i%2) x = x * a % m;
    return x;
}

void testcase(){
    using Modint = nachia::DynamicModint<0>;
    i64 D = 50000;
    vector<string> ans;
    vector<i64> ansx;
    vector<array<i64,3>> QPI;
    vector<i64> B;
    vector<i64> primes;
    for(i64 p=2; p<=D; p++) if(nachia::IsprimeExplicit(p)){
        primes.push_back(p);
        {
            i64 q = p; while(q*p <= D) q *= p;
            B.push_back(q);
        }
        for(i64 q=p; q<=D; q*=p){
            QPI.push_back({q,p,0});
            ansx.push_back(q);
        }
    }
    
    sort(QPI.begin(), QPI.end());
    sort(ansx.begin(), ansx.end());

    i64 T; cin >> T;
    vector<i64> inN(T);
    for(auto& t : inN) cin >> t;
    vector<vector<i64>> F(ansx.size() + 1);
    rep(i,T){
        i64 f = upper_bound(ansx.begin(), ansx.end(), inN[i]) - ansx.begin();
        inN[i] = f;
        F[f].push_back(i);
        //cout << "f=" << f << endl;
    }

    vector<string> R(F.size());
    R[0] = "1/1\n";

    //for(auto b : B) cout << b << " ";
    //cout << endl;

    i64 N = primes.size();
    vector<i64> Z(N, 1);
    vector<i64> A(N, 1);
    rep(i,QPI.size()) QPI[i][2] = i;
    for(auto [q,p,d] : QPI){
        //cout << "q = " << q << " , p = " << p << " , d = " << d << endl;
        rep(x,N){
            if(p != primes[x]) Z[x] = Z[x] * p % B[x];
            else A[x] = q;
        }
        //cout << "q = " << q << " , p = " << p << " , d = " << d << endl;
        if(F[d+1].size()){
            using M2 = nachia::StaticModint<998244353>;
            M2 f = 0;
            M2 g = 1;
            i64 n = 0; while(n<N && A[n]>1) n++;
            vector<i64> Q(n);
        //cout << "q = " << q << " , p = " << p << " , d = " << d << " , n = " << n << endl;
            rep(i,n){
                Modint::setMod(A[i]);
                Q[i] = Modint::raw(Z[i]%A[i]).inv().val();
                auto a = M2(A[i]).inv();
                //Q[i] = powm(Z[i]%A[i], A[i]/primes[i]*(primes[i]-1)-1, A[i]);
                f += a * M2(Q[i]);
                g *= a;
            }
        //cout << "q = " << q << " , p = " << p << " , d = " << d << endl;
            int p = (f - g).val();
            //cout << p << endl;
            string res;
            rep(i,n){
                if(i+p>=n){
                    res += to_string(Q[i] - A[i]);
                } else {
                    if(i) res += "+";
                    res += to_string(Q[i]);
                }
                res +="/";
                res += to_string(A[i]);
            }
            res += "\n";
            R[d] = res;
        }
    }
    rep(i,T){
        cout << R[inN[i]];
    }
}

int main(){
    ios::sync_with_stdio(false); cin.tie(nullptr);
    testcase();
    return 0;
}