/* -*- coding: utf-8 -*- * * 3412.cc: No.3412 Christmas Tree Coloring - yukicoder */ #include #include #include using namespace std; /* constant */ const int MAX_N = 200000; const int MOD = 998244353; const int CN = 3; const int CBITS = 1 << CN; const int CMSK = CBITS - 1; enum {R, G, B}; enum {RB = 1, GB = 2, BB = 4}; /* typedef */ using vi = vector; template struct MI { int v; MI(): v() {} MI(int _v): v(_v % MOD) { if (v < 0) v += MOD; } MI(long long _v): v(_v % MOD) { if (v < 0) v += MOD; } explicit operator int() const { return v; } MI operator+(const MI m) const { return MI(v + m.v); } MI operator-(const MI m) const { return MI(v + MOD - m.v); } MI operator-() const { return MI(MOD - v); } MI operator*(const MI m) const { return MI((long long)v * m.v); } MI &operator+=(const MI m) { return (*this = *this + m); } MI &operator-=(const MI m) { return (*this = *this - m); } MI &operator*=(const MI m) { return (*this = *this * m); } bool operator==(const MI m) const { return v == m.v; } bool operator!=(const MI m) const { return v != m.v; } MI pow(int n) const { // a^n % MOD MI pm = 1, a = *this; while (n > 0) { if (n & 1) pm *= a; a *= a; n >>= 1; } return pm; } MI inv() const { return pow(MOD - 2); } MI operator/(const MI m) const { return *this * m.inv(); } MI &operator/=(const MI m) { return (*this = *this / m); } }; using mi = MI; /* global variables */ vi nbrs[MAX_N]; int ps[MAX_N], cis[MAX_N]; mi dp[MAX_N][CBITS][CN], tmp[CBITS][CN]; /* subroutines */ /* main */ int main() { int n; scanf("%d", &n); for (int i = 1; i < n; i++) { int u, v; scanf("%d%d", &u, &v); u--, v--; nbrs[u].push_back(v); nbrs[v].push_back(u); } ps[0] = -1; for (int u = 0; u >= 0;) { auto &nbru = nbrs[u]; int up = ps[u]; if (cis[u] == 0) for (int c = 0; c < CN; c++) dp[u][1 << c][c] = 1; if (cis[u] < nbru.size()) { int v = nbru[cis[u]++]; if (v != up) { ps[v] = u; u = v; } } else { if (up >= 0) { for (int bits = 0; bits < CBITS; bits++) fill(tmp[bits], tmp[bits] + CN, 0); for (int bits = 0; bits < CBITS; bits++) for (int c = 0; c < CN; c++) if ((int)dp[u][bits][c]) for (int bits1 = 0; bits1 < CBITS; bits1++) for (int c1 = 0; c1 < CN; c1++) if (c1 != c && ! (bits1 & bits & BB)) tmp[bits | bits1][c1] += dp[up][bits1][c1] * dp[u][bits][c]; for (int bits = 0; bits < CBITS; bits++) copy(tmp[bits], tmp[bits] + CN, dp[up][bits]); } u = up; } } mi sum = 0; for (int c = 0; c < CN; c++) sum += dp[0][CMSK][c]; printf("%d\n", (int)sum); return 0; }