import std.conv, std.functional, std.range, std.stdio, std.string; import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons; import core.bitop; class EOFException : Throwable { this() { super("EOF"); } } string[] tokens; string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; } int readInt() { return readToken.to!int; } long readLong() { return readToken.to!long; } real readReal() { return readToken.to!real; } bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } } bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } } int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1; (unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; } int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); } int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); } struct ModInt(uint M_) { import std.conv : to; alias M = M_; uint x; this(ModInt a) { x = a.x; } this(uint x_) { x = x_ % M; } this(ulong x_) { x = x_ % M; } this(int x_) { x = ((x_ %= cast(int)(M)) < 0) ? (x_ + cast(int)(M)) : x_; } this(long x_) { x = cast(uint)(((x_ %= cast(long)(M)) < 0) ? (x_ + cast(long)(M)) : x_); } ref ModInt opAssign(T)(inout(T) a) if (is(T == uint) || is(T == ulong) || is(T == int) || is(T == long)) { return this = ModInt(a); } ref ModInt opOpAssign(string op, T)(T a) { static if (is(T == ModInt)) { static if (op == "+") { x = ((x += a.x) >= M) ? (x - M) : x; } else static if (op == "-") { x = ((x -= a.x) >= M) ? (x + M) : x; } else static if (op == "*") { x = cast(uint)((cast(ulong)(x) * a.x) % M); } else static if (op == "/") { this *= a.inv(); } else static assert(false); return this; } else static if (op == "^^") { if (a < 0) return this = inv()^^(-a); ModInt b = this, c = 1U; for (long e = a; e; e >>= 1) { if (e & 1) c *= b; b *= b; } return this = c; } else { return mixin("this " ~ op ~ "= ModInt(a)"); } } ModInt inv() const { uint a = M, b = x; int y = 0, z = 1; for (; b; ) { const q = a / b; const c = a - q * b; a = b; b = c; const w = y - cast(int)(q) * z; y = z; z = w; } assert(a == 1); return ModInt(y); } ModInt opUnary(string op)() const { static if (op == "+") { return this; } else static if (op == "-") { ModInt a; a.x = x ? (M - x) : 0U; return a; } else static assert(false); } ModInt opBinary(string op, T)(T a) const { return mixin("ModInt(this) " ~ op ~ "= a"); } ModInt opBinaryRight(string op, T)(T a) const { return mixin("ModInt(a) " ~ op ~ "= this"); } bool opCast(T: bool)() const { return (x != 0U); } string toString() const { return x.to!string; } } enum MO = 998244353; alias Mint = ModInt!MO; enum LIM = 2 * 260^^2 + 10; Mint[] inv, fac, invFac; void prepare() { inv = new Mint[LIM]; fac = new Mint[LIM]; invFac = new Mint[LIM]; inv[1] = 1; foreach (i; 2 .. LIM) { inv[i] = -((Mint.M / i) * inv[cast(size_t)(Mint.M % i)]); } fac[0] = invFac[0] = 1; foreach (i; 1 .. LIM) { fac[i] = fac[i - 1] * i; invFac[i] = invFac[i - 1] * inv[i]; } } Mint binom(long n, long k) { if (n < 0) { if (k >= 0) { return (-1)^^(k & 1) * binom(-n + k - 1, k); } else if (n - k >= 0) { return (-1)^^((n - k) & 1) * binom(-k - 1, n - k); } else { return Mint(0); } } else { if (0 <= k && k <= n) { assert(n < LIM); return fac[cast(size_t)(n)] * invFac[cast(size_t)(k)] * invFac[cast(size_t)(n - k)]; } else { return Mint(0); } } } void main() { prepare; try { for (; ; ) { const N = readInt(); auto U = new int[N - 1]; auto V = new int[N - 1]; auto L = new int[N - 1]; foreach (i; 0 .. N - 1) { U[i] = readInt - 1; V[i] = readInt - 1; L[i] = readInt; } const D = N * (N - 1) / 2 - (N - 2); const A = cast(int)(L.count(1)); const B = cast(int)(L.count(2)); auto as = new int[N]; auto bs = new int[N]; foreach (i; 0 .. N - 1) { if (L[i] == 1) { ++as[U[i]]; ++as[V[i]]; } if (L[i] == 2) { ++bs[U[i]]; ++bs[V[i]]; } } debug { writeln("D = ", D); writeln("A = ", A, ", B = ", B); writeln("as = ", as); writeln("bs = ", bs); } // debug {{ const n = (A + 1) * (B + 1); if (n <= 250) { int id(int a, int b) { return a * (B + 1) + b; } auto f = new Mint[][](n, n + 1); foreach (i; 0 .. n) { const a = i / (B + 1); const b = i % (B + 1); if (a == A && b == B) { f[i][0] = 1; } else { if (a > 0) { const prob = (Mint(a) / Mint(A + 2 * B)) * (1 - Mint((N - 1) - (a - 1) - b) / Mint(D)); f[i][id(a - 1, b)] += prob; f[i][id(a, b)] -= prob; } if (b > 0) { const prob = (Mint(2 * b) / Mint(A + 2 * B)) * (1 - Mint((N - 1) - a - (b - 1)) / Mint(D)); f[i][id(a, b - 1)] += prob; f[i][id(a, b)] -= prob; } if (a < A) { const prob = (Mint(A - a) / Mint(A + 2 * B)) * (Mint((N - 1) - a - b) / Mint(D)); f[i][id(a + 1, b)] += prob; f[i][id(a, b)] -= prob; } if (b < B) { const prob = (Mint(2 * (B - b)) / Mint(A + 2 * B)) * (Mint((N - 1) - a - b) / Mint(D)); f[i][id(a, b + 1)] += prob; f[i][id(a, b)] -= prob; } f[i][n] = 1; } } foreach (h; 0 .. n) { foreach (i; h .. n) { if (f[i][h]) { break; } } assert(f[h][h]); const s = f[h][h].inv; foreach (j; h + 1 .. n + 1) { f[h][j] *= s; } foreach (i; h + 1 .. n) { const t = f[i][h]; foreach (j; h + 1 .. n + 1) { f[i][j] -= t * f[h][j]; } } } foreach_reverse (i; 0 .. n) { foreach (j; i + 1 .. n) { f[i][n] -= f[i][j] * f[j][n]; } } debug { writeln("HELP"); foreach (a; 0 .. A + 1) { foreach (b; 0 .. B + 1) { if (b) write(" "); write(f[id(a, b)][n]); } writeln; } } Mint start, goal; foreach (u; 0 .. N) { start += f[id(as[u], bs[u])][n]; } if (A > 0) goal += A * f[id(1, 0)][n]; if (B > 0) goal += B * f[id(0, 1)][n]; goal += f[id(A, B)][n]; const brt = (goal - start) / N; // writeln("brt = ", brt); writeln(brt); } else { assert(false); } // }} } } catch (EOFException e) { } }