#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(i64 i=0; i<i64(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 <initializer_list> namespace nachia{ bool IsPrime(unsigned long long x) noexcept { if(x <= 1) return false; if(x % 2 == 0) return x == 2; using u64 = unsigned long long; using u128 = __uint128_t; u64 d = x-1; int s = 0; int q = 63; while(!(d&1)){ d >>= 1; s++; } while(!(d >> q)) q--; u64 r = x; for(int t=0; t<6; t++) r*=2-r*x; u128 n2 = -(u128)x % x; auto red = [=](u128 t) noexcept -> u64 { u64 t2 = (t + (u128)((u64)t*-r)*x) >> 64; return (t2 >= x || t2 < (t >> 64)) ? t2-x : t2; }; u64 one = red(n2); for(u64 base : { 2, 325, 9375, 28178, 450775, 9780504, 1795265022 }){ if(base%x==0) continue; u64 a = base = red(base%x*n2); for(int e=q-1; e>=0; e--){ a = red((u128)a*a); if((d>>e)&1) a = red((u128)a*base); } if(a == one) continue; for(int t=1; t<s&&a!=x-one; t++) a = red((u128)a*a); if(a != x-one) return false; } return true; } } // namespace nachia namespace nachia{ int Popcount(unsigned long long c) noexcept { #ifdef __GNUC__ return __builtin_popcountll(c); #else c = (c & (~0ull/3)) + ((c >> 1) & (~0ull/3)); c = (c & (~0ull/5)) + ((c >> 2) & (~0ull/5)); c = (c & (~0ull/17)) + ((c >> 4) & (~0ull/17)); c = (c * (~0ull/257)) >> 56; return c; #endif } // please ensure x != 0 int MsbIndex(unsigned long long x) noexcept { #ifdef __GNUC__ return 63 - __builtin_clzll(x); #else using u64 = unsigned long long; int q = (x >> 32) ? 32 : 0; auto m = x >> q; constexpr u64 hi = 0x88888888; constexpr u64 mi = 0x11111111; m = (((m | ~(hi - (m & ~hi))) & hi) * mi) >> 35; m = (((m | ~(hi - (m & ~hi))) & hi) * mi) >> 31; q += (m & 0xf) << 2; q += 0x3333333322221100 >> (((x >> q) & 0xf) << 2) & 0xf; return q; #endif } // please ensure x != 0 int LsbIndex(unsigned long long x) noexcept { #ifdef __GNUC__ return __builtin_ctzll(x); #else return MsbIndex(x & -x); #endif } } #include <utility> namespace nachia{ std::vector<std::pair<unsigned long long, int>> Factorize(unsigned long long x){ if(x == 1) return {}; if(IsPrime(x)) return {{x,1}}; using u64 = unsigned long long; using u128 = __uint128_t; u64 X = x; std::vector<u64> p; for(u64 i=2; i<100; i+=1+i%2) if(x%i==0){ p.push_back(i); while(x%i==0) x/=i; } u64 r=1; u128 n2=1; auto updX = [&](){ r = x; for(int t=0; t<6; t++) r*=2-r*x; n2 = -(u128)x % x; }; auto red = [&](u128 t) noexcept -> u64 { u64 s = ((u128)x*((u64)t*r)) >> 64; u64 t2 = t >> 64; return t2-s + (t2 < s ? x : 0); }; auto mult = [&](u64 a, u64 b) noexcept { return red((u128)red((u128)a*n2)*b); }; auto gcd = [](u64 a, u64 b) noexcept { if(!a || !b) return a|b; int q = LsbIndex(a|b); b >>= LsbIndex(b); a >>= LsbIndex(a); while(a!=b){ if(a<b){ b-=a; b>>=LsbIndex(b); } else{ a-=b; a>>=LsbIndex(a); } } return a<<q; }; static u64 v = 7001; p.push_back(x); for(int pi=p.size()-1; pi<(int)p.size(); pi++) while(p[pi] != 1 && !IsPrime(p[pi])){ x = p[pi]; updX(); while(p[pi] == x){ v^=v<<13; v^=v>>7; v^=v<<17; // Xorshift https://www.jstatsoft.org/article/download/v008i14/916 u64 c = red(v); if(c == 0) continue; auto f = [=](u64 a) noexcept -> u64 { return red((u128)a*a+c); }; u64 a=0, b=f(a); u64 buf = 1, sz = 1, nx = 10; while(true){ while(nx != sz && a != b){ buf = mult(buf, a<=b?b-a:a-b); sz++; a = f(a); b = f(f(b)); } u64 g = gcd(buf, x); if(g != 1){ while(p[pi] % g == 0) p[pi] /= g; p.push_back(g); break; } if(a == b) break; nx = sz * 3 / 2; } } } std::vector<std::pair<u64, int>> res; for(u64 q : p) if(q != 1){ int e=0; while(X%q == 0){ e++; X/=q; } if(e) res.push_back({ q, e }); } return res; } unsigned long long Totient(unsigned long long x){ auto F = Factorize(x); for(auto f : F) x -= x / f.first; return x; } unsigned long long NumDivisors(unsigned long long x){ auto F = Factorize(x); unsigned long long res = 1; for(auto f : F) res *= f.second + 1; return res; } } // namespace nachia namespace nachia{ template<class Int> Int Gcd(Int a, Int b){ if(a < 0) a = -a; if(b < 0) b = -b; if(!a || !b) return a + b; while(b){ a %= b; std::swap(a, b); } return a; } } string q2(){ i64 q = 1ll << 40; string s = to_string(q); string t = s; reverse(t.begin(), t.end()); t += string(40, '0'); t += s; return t; } string q5(){ i64 q = 5ll * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5; string s = to_string(q); string t = s; reverse(t.begin(), t.end()); t += string(20, '0'); t += s; return t; } void testcase(){ i64 N; cin >> N; string q = q2(); if(N%5 == 0) q = q5(); while(N%2 == 0) N /= 2; while(N%5 == 0) N /= 5; i64 phi = nachia::Totient(N); if(phi == 1){ cout << 1 << "\n"; cout << q << " " << 1 << "\n"; } else { i64 t = q.size(); auto qq = q; while(nachia::Gcd(t, phi) != 1){ t++; qq.push_back('0'); } reverse(qq.begin(), qq.end()); cout << 2 << "\n"; cout << q << " " << 1 << "\n"; cout << qq << " " << (phi-1) << "\n"; } } int main(){ ios::sync_with_stdio(false); cin.tie(nullptr); rep(t,3) testcase(); return 0; }