#include<bits/stdc++.h>
using namespace std;
using ll = long long;

ll comb[1001][1001];
void solve(){
    ll m;
    cin>>m;
    set<pair<ll,ll>> ans;
    ans.insert(make_pair(m,1));
    ans.insert(make_pair(m,m-1));
    for(int i = 1;i<=1000;i++){
        for(int j = 0;j<=1000;j++){
            if(comb[i][j]==m) ans.insert(make_pair(i,j));
        }
    }
    for(ll k = 2;k<=7;k++){
        ll now = 1;
        for(ll i = 1;i<=k;i++) now *= i;
        ll right = 1e9+10;
        ll left = k;
        while(right-left>1){
            ll mid = (right+left)/2;
            ll kk = 1;
            for(int i = 0;i<k;i++){
                if(kk>(ll)1e18/((mid-i))) {
                    kk = -1;
                    break;
                }
                kk *= mid - i;
            }
            if(kk==-1){
                right = mid;
                continue;
            }
            kk /= now;
            if(kk==m){
                ans.insert(make_pair(mid,k));
                ans.insert(make_pair(mid,mid-k));
            }
            if(kk<=m) left = mid;
            else right = mid;
        }
    }
    cout<<ans.size()<<endl;
    int cnt = 0;
    for(auto&itr:ans){
        if(cnt++) cout<<" ";
        cout<<"("<<itr.first<<","<<itr.second<<")";
    }
    cout<<endl;
        
}

int main(){
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    comb[1][0] = comb[1][1] = 1;
    for(int i = 2;i<=1000;i++){
        comb[i][0] = comb[i][i] = 1;
        for(int j = 1;j<i;j++){
            if(comb[i-1][j]==-1) continue;
            if(comb[i-1][j-1]==-1) continue;
            if(comb[i-1][j]+comb[i-1][j-1]>=2e15) {
                comb[i][j] = -1;
                continue;
            }
            comb[i][j] = comb[i-1][j] + comb[i-1][j-1];
        }
    }

    int t;
    cin>>t;
    while(t--){
        solve();
    }
}