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)(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; void main() { debug { foreach (p; 0 .. 1 << 6) { foreach (q; 0 .. 1 << 6) { if ((p & 1) == (q & 1)) { auto a = new int[][](6, 6); foreach (x; 0 .. 6) { a[x][0] = (p >> x) & 1; } foreach (y; 0 .. 6) { a[0][y] = (q >> y) & 1; } foreach (x; 1 .. 6) foreach (y; 1 .. 6) { a[x][y] = a[x - 1][y - 1] ^ a[x - 1][y] ^ a[x][y - 1]; } bool ok = true; foreach (i; 0 .. 6 + 1) foreach (j; i + 2 .. 6 + 1) { foreach (k; 0 .. 6 + 1) foreach (l; k + 2 .. 6 + 1) { int sum; foreach (x; i .. j) foreach (y; k .. l) { sum ^= a[x][y]; } ok = ok && (sum % 2 == 0); } } if (ok) { writeln(a); } } } } } try { for (; ; ) { const N = readInt(); const M = readInt(); auto X = new int[M]; auto Y = new int[M]; auto Z = new int[M]; foreach (i; 0 .. M) { X[i] = readInt() - 1; Y[i] = readInt() - 1; Z[i] = readInt() ^ 1; } Mint ans; if (N == 1) { ans = Mint(2)^^(N - M); } else if (N == 2) { foreach (p; 0 .. 1 << 4) { if (popcnt(p) % 2 == 0) { bool ok = true; foreach (i; 0 .. M) { ok = ok && (((p >> (X[i] * 2 + Y[i])) & 1) == Z[i]); } if (ok) { ans += 1; } } } } else if (N <= 5) { foreach (a00; 0 .. 2) { foreach (p; 0 .. 1 << N) foreach (q; 0 .. 1 << N) { if (!(p & 1) && !(q & 1)) { bool even = true; foreach (i; 0 .. N + 1) foreach (j; i + 2 .. N + 1) { foreach (k; 0 .. N + 1) foreach (l; k + 2 .. N + 1) { if ((j - i) % 2 != 0 && (l - k) % 2 != 0) { even = even && ((a00 + popcnt((p & ((1 << j) - 1)) >> i) + popcnt((q & ((1 << l) - 1)) >> k)) % 2 == 0); } } } if (even) { debug { writefln("even %b %0*b %0*b", a00, N, p, N, q); } bool ok = true; foreach (i; 0 .. M) { ok = ok && ((a00 ^ ((p >> X[i]) & 1) ^ ((q >> Y[i]) & 1)) == Z[i]); } if (ok) { ans += 1; } } } } } } else { if (Z.all!"a == 0") { ans += 1; } } writeln(ans); break; } } catch (EOFException e) { } }