// Ice cream? I scream!
#include <bits/stdc++.h>
#ifdef ONLINE_JUDGE
	#define freopen Chitanda
#endif
#define wjy namespace
#define xsy std
typedef long long ll;
using wjy xsy;

template<typename T> void debug(string s, T x) {cerr << " " << s << " = " << x << " \n";}
template<typename T, typename... Args> void debug(string s, T x, Args... args) {for (int i = 0, b = 0; i < (int)s.size(); i++) if (s[i] == '(' || s[i] == '{') b++;else if (s[i] == ')' || s[i] == '}') b--;else if (s[i] == ',' && b == 0) {cerr << " " << s.substr(0, i) << " = " << x << " |";debug(s.substr(s.find_first_not_of(' ', i + 1)), args...);break;}}
#ifdef ONLINE_JUDGE
	#define Debug(...)
#else
	#define Debug(...) debug(#__VA_ARGS__, __VA_ARGS__)
#endif

const int MAXN = 200;
const int BASE = 10007;
const int MOD = 998244353;
const int BASE1 = 9997;
const int MOD1 = 1e9 + 7;

int n, m;

void Ope(int *a, int *b, int *c)
{
	for (int i = 1; i <= n; i++)
		c[i] = a[b[i]];
}

void IOpe(int *a, int *b, int *c)
{
	for (int i = 1; i <= n; i++)
		a[b[i]] = c[i];
}

pair<int, int> Hsh(int *a)
{
	int res = 0, cur = 1;
	for (int i = 1; i <= n; i++)
	{
		res = (res + 1ll * cur * a[i] % MOD) % MOD;
		cur = 1ll * cur * BASE % MOD;
	}
	int res1 = 0, cur1 = 1;
	for (int i = 1; i <= n; i++)
	{
		res1 = (res1 + 1ll * cur1 * a[i] % MOD1) % MOD1;
		cur1 = 1ll * cur1 * BASE1 % MOD1;
	}
	return make_pair(res, res1);
}

int a[MAXN][MAXN], c[MAXN], tmp[MAXN];
bool ch[MAXN];
set<pair<int, int> > ans;

void Dfs1(int pos)
{
	if (pos > m)
	{
		for (int i = 1; i <= n; i++)
			c[i] = i;
		bool flg = true;
		for (int i = 1; i <= m; i++)
		{
			if (ch[i])
			{
				flg = false;
				Ope(c, a[i], tmp);
				memcpy(c, tmp, sizeof(tmp));
			}
		}
		if (flg)
			return;
//		for (int i = 1; i <= n; i++)
//		 	printf("%d ", c[i]);
//		puts("");
		ans.insert(Hsh(c));
		return;
	}
	Dfs1(pos + 1);
	ch[pos] = true;
	Dfs1(pos + 1);
	ch[pos] = false;
}

map<pair<int, int>, bool> ok[MAXN];
int cur[MAXN];

bool Dfs3(int pos)
{
	auto nw = Hsh(cur);
	if (ok[pos].find(nw) != ok[pos].end())
		return ok[pos][nw];
	if (!pos)
		return false;
	if (Hsh(a[pos]) == nw)
		return ok[pos][nw] = true;
	if (Dfs3(pos - 1))
		return ok[pos][nw] = true;
	IOpe(tmp, a[pos], cur);
	int tt[10];
	memcpy(tt, cur, sizeof(int) * (n + 1));
	memcpy(cur, tmp, sizeof(int) * (n + 1));
	if (Dfs3(pos - 1))
		return ok[pos][nw] = true;
	memcpy(cur, tt, sizeof(int) * (n + 1));
	return ok[pos][nw] = false;
}

int tot;
int p[MAXN];
bool used[MAXN];

int Check()
{
	memcpy(cur, p, sizeof(p));
	return (int)(Dfs3(m));
}

void Dfs2(int pos)
{
	if (pos > n)
		return void(tot += Check());
	for (int i = 1; i <= n; i++)
	{
		if (!used[i])
		{
			used[i] = true;
			p[pos] = i;
			Dfs2(pos + 1);
			used[i] = false;
		}
	}
}

signed main()
{
	scanf("%d%d", &n, &m);
	for (int i = 1; i <= m; i++)
		for (int j = 1; j <= n; j++)
			scanf("%d", a[i] + j);
	if (n > 8)
	{
		Dfs1(1);
		printf("%zu\n", ans.size() % MOD1);
	}
	else
	{
		Dfs2(1);
		printf("%d\n", tot % MOD1);
	}
	return 0;
}