#include #include using namespace std; using ll = long long; using pii = pair; using pll = pair; using vi = vector; using vl = vector; #define rep3(i, a, b, c) for (ll i = (a); i < (b); i += (c)) #define rep2(i, a, b) rep3(i, a, b, 1) #define rep1(i, n) rep2(i, 0, n) #define rep0(n) rep1(aaaaa, n) #define ov4(a, b, c, d, name, ...) name #define rep(...) ov4(__VA_ARGS__, rep3, rep2, rep1, rep0)(__VA_ARGS__) #define per(i, a, b) for (ll i = (a) - 1; i >= (b); i--) #define fore(e, v) for (auto &&e : v) #define all(a) begin(a), end(a) #define sz(a) (int)(size(a)) #define lb(v, x) (lower_bound(all(v), x) - begin(v)) #define eb emplace_back template bool chmin(T &a, const S &b) { return a > b ? a = b, 1 : 0; } template bool chmax(T &a, const S &b) { return a < b ? a = b, 1 : 0; } const int INF = 1e9 + 100; const ll INFL = 3e18 + 100; #define i128 __int128_t struct _ { _() { cin.tie(0)->sync_with_stdio(0), cout.tie(0); } } __; int main() { ll N; cin >> N; const int MAX_SQRT_N = 1'000'007; using al3 = array; vector ans; rep(i, 1, MAX_SQRT_N) { if (i * i > N) break; if (N % i == 0) { if (i % 2) { ll L = N / i - i / 2, R = N / i + i / 2; if (L > 0) ans.push_back(al3{1, L, R}); L = i / 2 - N / i + 1, R = i / 2 + N / i; if (L > 0) ans.push_back(al3{1, L, R}); } if (N != i * i && (N / i) % 2) { ll L = i - N / i / 2, R = i + N / i / 2; if (L > 0) ans.push_back(al3{1, L, R}); L = N / i / 2 - i + 1, R = N / i / 2 + i; if (L > 0) ans.push_back(al3{1, L, R}); } } } rep(e, 2, 40) { ll s = 0, r = 0, l = 0; auto ipow = [&](ll a, ll n) -> ll { ll ret = 1; rep(i, n) { ret *= a; if (ret > N) break; } return ret; }; while (ipow(r, e) <= N) { while (s > N) s -= ipow(l++, e); if (s == N) ans.push_back(al3{e, l, r}); s += ipow(++r, e); } } sort(all(ans)); ans.erase(unique(all(ans)), ans.end()); cout << sz(ans) << '\n'; for (auto [e, l, r] : ans) cout << e << ' ' << l << ' ' << r << '\n'; }