#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template pair operator+(const pair &l, const pair &r) { return make_pair(l.first + r.first, l.second + r.second); } template pair operator-(const pair &l, const pair &r) { return make_pair(l.first - r.first, l.second - r.second); } template vector sort_unique(vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template istream &operator>>(istream &is, vector &vec) { for (auto &v : vec) is >> v; return is; } template ostream &operator<<(ostream &os, const vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } #if __cplusplus >= 201703L template istream &operator>>(istream &is, tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template ostream &operator<<(ostream &os, const tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } #endif template ostream &operator<<(ostream &os, const deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template ostream &operator<<(ostream &os, const set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const pair &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; } template ostream &operator<<(ostream &os, const map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template ostream &operator<<(ostream &os, const unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl #define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr) #else #define dbg(x) (x) #define dbgif(cond, x) 0 #endif struct GridUnionFind { int H, W; std::vector par, cou; using P = std::pair; GridUnionFind(int H_, int W_) : H(H_), W(W_), par(H * W), cou(H * W, 1) { std::iota(par.begin(), par.end(), 0); } inline int id_(int h, int w) { return h * W + w; } inline bool coordinate_valid(int h, int w) { return h >= 0 and h < H and w >= 0 and w < W; } int _find(int x) { return (par[x] == x) ? x : (par[x] = _find(par[x])); } bool _unite(int x, int y) { x = _find(x), y = _find(y); if (x == y) return false; if (cou[x] < cou[y]) std::swap(x, y); par[y] = x, cou[x] += cou[y]; return true; } int find(int h, int w) { assert(coordinate_valid(h, w)); return _find(id_(h, w)); } bool unite(int h, int w, int h2, int w2) { assert(coordinate_valid(h, w) and coordinate_valid(h2, w2)); return _unite(id_(h, w), id_(h2, w2)); } int count(int h, int w) { return cou[find(h, w)]; } bool same(int h, int w, int h2, int w2) { return find(h, w) == find(h2, w2); } int find(P p) { return find(p.first, p.second); } bool unite(P p, P p2) { return unite(p.first, p.second, p2.first, p2.second); } int count(P p) { return count(p.first, p.second); } bool same(P p, P p2) { return same(p.first, p.second, p2.first, p2.second); } void merge_outer() { for (int h = 0; h < H - 1; h++) unite(h, 0, h + 1, 0), unite(h, W - 1, h + 1, W - 1); for (int w = 0; w < W - 1; w++) unite(0, w, 0, w + 1), unite(H - 1, w, H - 1, w + 1); } template friend OStream &operator<<(OStream &os, GridUnionFind &g) { constexpr int WW = 3; os << "[(" << g.H << " * " << g.W << " grid)\n"; for (int i = 0; i < g.H; i++) { for (int j = 0; j < g.W - 1; j++) { os << std::setw(WW) << g.find(i, j) << (g.same(i, j, i, j + 1) ? '-' : ' '); } os << std::setw(WW) << g.find(i, g.W - 1) << '\n'; if (i < g.H - 1) { for (int j = 0; j < g.W; j++) os << std::setw(WW + 1) << (g.same(i, j, i + 1, j) ? "| " : " "); os << "\n"; } } os << "]\n"; return os; } }; lint solve(int H, int W, int K) { lint ret = 0; REP(dx, H) REP(dy, W) { GridUnionFind uf(H, W); REP(i, H) REP(j, W) { uf.unite(i, j, (i + dx) % H, (j + dy) % W); } vector roots; REP(i, H) REP(j, W) { roots.push_back(uf.find(i, j)); } roots = sort_unique(roots); dbg((vector{dx, dy, int(roots.size())})); lint t = 1; for (auto _ : roots) t *= K; ret += t; } return ret / (H * W); } int main() { int H, W, K; cin >> H >> W >> K; if (K == 1) { puts("1"); } else if (K == 2) { cout << solve(H, W, K) - 2 << endl; } else { cout << solve(H, W, 3) - solve(H, W, 2) * 3 + 3 << endl; } }