#include #include using namespace std; using namespace atcoder; #define rep(i, n) for (long long i = 0; i < (long long)(n); i++) #define rrep(i,start,end) for (long long i = start;i >= (long long)(end);i--) #define repn(i,end) for(long long i = 0; i <= (long long)(end); i++) #define reps(i,start,end) for(long long i = start; i < (long long)(end); i++) #define repsn(i,start,end) for(long long i = start; i <= (long long)(end); i++) #define each(p,a) for(auto &p:a) typedef long long ll; typedef unsigned long long ull; typedef long double ld; typedef vector vll; typedef vector> vpll; typedef vector> vvll; typedef set sll; typedef map mpll; typedef pair pll; typedef tuple tpl3; #define LL(...) ll __VA_ARGS__; input(__VA_ARGS__) #define LD(...) ld __VA_ARGS__; input(__VA_ARGS__) #define Str(...) string __VA_ARGS__; input(__VA_ARGS__) #define Ch(...) char __VA_ARGS__; input(__VA_ARGS__) #define all(a) (a).begin(),(a).end() #define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() ); #define sz(x) (int)x.size() // << std::fixed << std::setprecision(10) const ll INF = 1LL << 60; const ld EPS = 1e-9; inline ll lfloor(ll x,ll m){return (x - ((x % m+ m)%m))/m;} inline ll positive_mod(ll a,ll m){return (a % m + m)%m;} inline ll popcnt(ull a){ return __builtin_popcountll(a);} //0indexed inline ll topbit(ll a){assert(a != 0);return 63 - __builtin_clzll(a);} inline ll smlbit(ll a){assert(a != 0);return __builtin_ctzll(a);} template bool chmin(T& a, T b){if(a > b){a = b;return true;}return false;} template bool chmax(T& a, T b){if(a < b){a = b;return true;}return false;} template std::istream &operator>>(std::istream&is,std::vector&v){for(T &in:v){is>>in;}return is;} template std::ostream &operator<<(std::ostream&os,const std::vector&v){for(auto it=std::begin(v);it!=std::end(v);){os<<*it<<((++it)!=std::end(v)?" ":"");}return os;} templatestd::ostream &operator<< (std::ostream &os, std::pair p){os << "{" << p.first << "," << p.second << "}";return os;} templatevoid input(T&... a){(cin >> ... >> a);} void print(){cout << endl;} templatevoid print(const T& a, const Ts&... b){cout << a;((cout << ' ' << b), ...);cout << endl;} template void pspace(const T& a){ cout << a << ' ';} void perr(){cerr << endl;} templatevoid perr(const T& a, const Ts&... b){cerr << a;((cerr << ' ' << b), ...);cerr << endl;} void yes(bool i = true){ return print(i?"yes":"no"); } void Yes(bool i = true){ return print(i?"Yes":"No"); } void YES(bool i = true){ return print(i?"YES":"NO"); } template vector &operator++(vector &v) {for(auto &e : v) e++;return v;} template vector operator++(vector &v, signed) {auto res = v;for(auto &e : v) e++;return res;} template vector &operator--(vector &v) {for(auto &e : v) e--;return v;} template vector operator--(vector &v, signed) {auto res = v;for(auto &e : v) e--;return res;} //grid探索用 vector _ta = {0,0,1,-1,1,1,-1,-1}; vector _yo = {1,-1,0,0,1,-1,1,-1}; bool isin(ll now_i,ll now_j,ll h,ll w){return (0<=now_i && now_i < h && 0 <= now_j && now_j < w);} ll lpow(ll x,ll n){ll ans = 1;while(n >0){if(n & 1)ans *= x;x *= x;n >>= 1;}return ans;} ll Modlpow(ll x,ll n,ll m){ll ans = 1;ll a = x%m;while(n >0){if(n & 1){ans *= a;ans%= m;}a *= a;a %= m;n >>= 1;}return ans;} const ll MOD9 = 998244353LL; const ll MOD10 = 1000000007LL; int main(){ ios::sync_with_stdio(false);cin.tie(nullptr); //前処理、約数列挙PまでO(PlogP) //昇順でない ll P = 2 * lpow(10,5) + 1; vector> primeFact(P+1); vector Deleted(P+1,0); Deleted[1] = 1; repsn(i,2,P){ if(Deleted[i] != 0) continue; for(int j = i;j <= P;j += i){ if(Deleted[j] !=0)continue; Deleted[j] = i;//iで初めに割られたということ } } repsn(i,1,P){ primeFact[i].push_back(i); ll now = i; while(Deleted[now] != now){ now /= Deleted[now]; primeFact[i].push_back(now); } if(i != 1){ primeFact[i].push_back(1); } } vll so; repsn(i,2,P){ if(primeFact[i].size() <= 2){ so.push_back(i); } } LL(x); if(x == 1){ cout << 2 << endl; cout << "1 2" << endl; cout << "b g" << endl; return 0; } vll sm; each(p,so){ while(x % p == 0){ x /= p; sm.push_back(p); } if(p == 2){ vll tmp; while(sm.size() >= 2 ){ sm.pop_back(); sm.pop_back(); tmp.push_back(4); } rep(z,tmp.size()){ sm.push_back(4); } } } if(x != 1){ sm.push_back(x); } ll n = reduce(all(sm)) + (ll)sm.size(); if(reduce(all(sm)) + (ll)sm.size() > 2 * lpow(10,5)){ cout << -1 << endl; return 0; } ll tya = sm.size(); ll cnt= 0; cout << n << endl; rep(i,tya){ if(i != 0){ cout << i << " " << i+1 << endl; } rep(j,sm[i]){ cout << i+1 << " " << tya+1 + cnt << " " << endl; cnt++; } } rep(i,tya){ pspace('b'); } rep(i,n-tya){ pspace('g'); } print(); }