#include <bits/stdc++.h>
using namespace std;

const int maxn = 24, maxm = maxn * maxn * maxn, mod = 998244353;
int n, m;
tuple<int, int, int> abc[maxm];
set<vector<int>> st;
bitset<(1<<maxn) * maxn> bst;
int dp[1<<maxn][maxn];
int ans;

int cut(int mask, int l, int r) {
	return (mask >> l) & ((1 << (r-l+1)) - 1);
}

void modadd(int &a, int b) {
	a += b;
	if (a >= mod) a -= mod;
}

void set_true(int mask, int i) {
	bst[mask * maxn + i] = true;
}

bool invalid(int mask, int i) {
	return bst[mask * maxn + i];
}

bool eq(tuple<int, int, int> &t1, tuple<int, int, int> &t2) {
	auto &[a1, b1, c1] = t1;
	auto &[a2, b2, c2] = t2;
	// if (a1 != a2 || c1 != c2) return false;
	// bool pb = (b1 < a1 && b2 < a2) || (b1 > a1 && b1 < c1 && b2 > a2 && b2 < c2) || (b1 > c1 && b2 > c2);
	// return pb;
	return (a1 == a2 && c1 == c2);
}

int main() {
	ios_base::sync_with_stdio(0); cin.tie(0);
	cin >> n >> m;
	for (int i=0; i<m; i++) {
		int a, b, c;
		cin >> a >> b >> c;
		a--, b--, c--;
		abc[i] = {a, b, c};
	}

	for (int i=0; i<m; i++) {
		auto &[a, b, c] = abc[i];
		vector<int> v = {a, b, c};
		sort(v.begin(), v.end());
		if (st.count(v)) {
			cout << "0\n";
			return 0;
		}
		st.insert(v);
	}

	sort(abc, abc + m, [](tuple<int, int, int> &t1, tuple<int, int, int> &t2) {
		auto &[a1, b1, c1] = t1;
		auto &[a2, b2, c2] = t2;
		if (a1 != a2) return a1 < a2;
		if (c1 != c2) return c1 < c2;
		return b1 < b2;
	});
	for (int l=0; l<m; ) {
		int r = l;
		while (r < m && eq(abc[l], abc[r])) r++;

		// gaboleh ke b kalo a dan c sama
		auto &[a, _, c] = abc[l];
		if (a > c) swap(a, c);
		for (int mask=0; mask<(1<<(n-2)); mask++) {
			int true_mask = 0;

			if (a > 0) true_mask |= cut(mask, 0, a - 1);
			if (a + 1 <= c - 1) true_mask |= (cut(mask, a, c - 2) << (a + 1));
			if (c + 1 <= n - 1) true_mask |= (cut(mask, c - 1, n - 3) << (c + 1));
			true_mask &= ~(1 << b);
			for (int i=l; i<r; i++) {
				auto &[aa, b, cc] = abc[i];
				set_true(true_mask, b);
			}

			true_mask |= (1 << a);
			true_mask |= (1 << c);
			for (int i=l; i<r; i++) {
				auto &[aa, b, cc] = abc[i];
				set_true(true_mask, b);
			}
		}

		l = r;
	}

	for (int mask=1; mask<(1<<n); mask++) {
		if ((mask&(mask-1)) == 0) {
			int i = 31 - __builtin_clz(mask);
			dp[mask][i] = !invalid(0, i); // cek dulu i pernah jadi b atau nggak
		} else {
			for (int m1=mask; m1>0; m1-=m1&-m1) {
				int i = __builtin_ctz(m1);
				dp[mask][i] = 0;
				int pre_mask = mask & ~(1 << i);
				for (int m2=pre_mask; m2>0; m2-=m2&-m2) {
					int j = __builtin_ctz(m2);
					if (!invalid(pre_mask, i)) modadd(dp[mask][i], dp[pre_mask][j]);
				}
			}
		}
	}

	ans = 0;
	for (int i=0; i<n; i++) modadd(ans, dp[(1<<n)-1][i]);
	cout << ans << '\n';
}

answer.code: In function ‘int main()’:
answer.code:79:45: error: ‘b’ was not declared in this scope
   79 |                         true_mask &= ~(1 << b);
      |                                             ^