#include namespace { #pragma GCC diagnostic ignored "-Wunused-function" #include #pragma GCC diagnostic warning "-Wunused-function" using namespace std; using namespace atcoder; #define rep(i,n) for(int i = 0; i < (int)(n); i++) #define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; i--) #define all(x) begin(x), end(x) #define rall(x) rbegin(x), rend(x) template bool chmax(T& a, const T& b) { if (a < b) { a = b; return true; } else return false; } template bool chmin(T& a, const T& b) { if (b < a) { a = b; return true; } else return false; } using ll = long long; using P = pair; using VI = vector; using VVI = vector; using VL = vector; using VVL = vector; template vector divisors(T x) { vector res1, res2; T d = 1; for(; d * d < x; d++) { if (x % d == 0) { res1.emplace_back(d); res2.emplace_back(x / d); } } if (d * d == x) res1.emplace_back(d); res1.insert(res1.end(), res2.rbegin(), res2.rend()); return res1; } } int main() { ios::sync_with_stdio(false); cin.tie(0); using I = __int128; ll n; cin >> n; vector> ans; for (int e = 1;; e++) { if (e == 1) { // (r-l+1)(l+r)/2 for (ll d1 : divisors(2 * n)) { ll d2 = 2 * n / d1; if (d1 % 2 == d2 % 2) continue; ll l = (d2 - d1 + 1) / 2; ll r = (d1 + d2 - 1) / 2; if (1 <= l && l <= r) ans.emplace_back(e, l, r); } } else { if (1LL << e > n) break; vector s{0}; for (int i = 1;; i++) { ll ie = 1; constexpr long long INF = 1002003004005006007; rep(_, e) if (__builtin_mul_overflow(ie, i, &ie)) { ie = INF; break; } if (ie > n) break; s.emplace_back(s.back() + ie); } int sz = s.size(); int l = 0; rep(r, sz) { while (s[r] - s[l] > n) l++; if (s[r] - s[l] == n) ans.emplace_back(e, l + 1, r); } } } cout << ans.size() << '\n'; for (auto [e, l, r] : ans) cout << e << ' ' << l << ' ' << r << '\n'; }