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const ll N = 3e5 + 10;

namespace ACAUTOMATON {
	class ACAutomaton {
	public:
		ll cnt = 0, nxt[N][26], jl[N], fail[N], f[N];
	public:
		inline void Clear () {
			_for (i, 0, cnt) {
				memset (nxt[i], 0, sizeof (nxt[i]));
				fail[i] = f[i] = jl[i] = 0;
			}
			cnt = 0;
			return;
		}
		inline void Insert (std::string s) {
			ll p = 0, len = s.length () - 1;
			_for (i, 0, len) {
				ll c = s[i] - 'a';
				if (!nxt[p][c]) nxt[p][c] = ++cnt;
				p = nxt[p][c];
			}
			return;
		}
		inline void Build () {
			std::queue <ll> q;
			_for (i, 0, 25) if (nxt[0][i]) fail[nxt[0][i]] = 0, q.push (nxt[0][i]);
			while (!q.empty ()) {
				ll u = q.front (); q.pop ();
				_for (i, 0, 25) {
					if (nxt[u][i]) fail[nxt[u][i]] = nxt[fail[u]][i], q.push (nxt[u][i]);
					else nxt[u][i] = nxt[fail[u]][i];
				}
			}
			return;
		}
		inline ll GetAns (std::string s, ll w) {
			ll p = 0, len = s.length () - 1, num = 0;
			_for (i, 0, len) {
				ll c = s[i] - 'a';
				jl[nxt[p][c]] = 1;
				if (jl[fail[nxt[p][c]]]) f[nxt[p][c]] = std::max (f[nxt[p][c]], f[fail[nxt[p][c]]]);
				num = std::max (num, f[nxt[p][c]]);
				p = nxt[p][c];
			}
			return f[p] = std::max (f[p], num + w);
		}
	};
}

namespace SOLVE {
	ll n, m, w[N], ans; std::string s[N];
	ACAUTOMATON::ACAutomaton ac;
	inline ll rnt () {
		ll x = 0, w = 1; char c = getchar ();
		while (!isdigit (c)) { if (c == '-') w = -1; c = getchar (); }
		while (isdigit (c)) x = (x << 3) + (x << 1) + (c ^ 48), c = getchar ();
		return x * w;
	}
	inline void In () {
		ac.Clear ();
		n = rnt (), ans = 0;
		_for (i, 1, n) {
			std::cin >> s[i], w[i] = rnt ();
			if (w < 0) continue;
			ac.Insert (s[i]);
		}
		return;
	}
	inline void Solve () {
		ac.Build ();
		_for (i, 1, n) {
			if (w[i] < 0) continue;
			ans = std::max (ans, ac.GetAns (s[i], w[i]));
		}
		return;
	}
	inline void Out () {
		printf ("%lld\n", ans);
		return;
	}
}

namespace ACAUTOMATON {
	class ACAutomaton {
	private:
		ll cnt = 0, tot = 1, nxt[N][26], fail[N], end[N], f[N][30][M], jl[N][30][M][2];
		class APJifengc { public: ll u, l, s; };
		std::pair <ll, ll> vis[30 * 45];
		std::vector <ll> answer;
		char temp[N];
	public:
		inline void Insert (char *s, ll id) {
			ll p = 0, len = strlen (s + 1);
			_for (i, 1, len) {
				ll c = s[i] - 'a';
				if (!nxt[p][c]) nxt[p][c] = ++cnt;
				p = nxt[p][c];
			}
			end[p] |= 1 << (id - 1);
			return;
		}
		inline void Build () {
			std::queue <ll> q;
			_for (i, 0, 25) if (nxt[0][i]) fail[nxt[0][i]] = 0, q.push (nxt[0][i]);
			while (!q.empty ()) {
				ll u = q.front (); q.pop ();
				_for (i, 0, 25) {
					if (nxt[u][i]) fail[nxt[u][i]] = nxt[fail[u]][i], end[nxt[u][i]] |= end[nxt[fail[u]][i]], q.push (nxt[u][i]);
					else nxt[u][i] = nxt[fail[u]][i];
				}
			}
			return;
		}
		inline ll BFS (ll target,ll m) {
			std::queue <APJifengc> q;
			ll ans = 0; f[0][0][0] = 1;
			q.push ((APJifengc){0, 0, 0});
			while (!q.empty ()) {
				ll u = q.front ().u, l = q.front ().l, s = q.front ().s; q.pop ();
				if (l > m) break;
				if (s == target && l == m) ans += f[u][l][s];
				_for (i, 0, 25) {
					ll v = nxt[u][i], ln = l + 1, st = s | end[v];
					if (!f[v][ln][st]) q.push ((APJifengc){v, ln, st});
					f[v][ln][st] += f[u][l][s];
				}
			}
			return ans;
		}
		inline ll DFS (ll u, ll l, ll s, ll target, ll m) {
			if (jl[u][l][s][0]) return jl[u][l][s][1];
			jl[u][l][s][0] = 1;
			if (l == m) return jl[u][l][s][1] = (s == target);
			_for (i, 0, 25) jl[u][l][s][1] |= DFS (nxt[u][i], l + 1, s | end[nxt[u][i]], target, m);
			return jl[u][l][s][1];
		}
		inline void PrintAns (ll u, ll l, ll s, ll m) {
			if (!jl[u][l][s][1]) return;
			if (l == m) { puts (temp + 1); return; }
			_for (i, 0, 25) temp[l + 1] = i + 'a', PrintAns (nxt[u][i], l + 1, s | end[nxt[u][i]], m);
			return;
		}
	};
}

namespace SOLVE {
	ll n, m, ans; char s[20];
	ACAUTOMATON::ACAutomaton ac;
	inline ll rnt () {
		ll x = 0, w = 1; char c = getchar ();
		while (!isdigit (c)) { if (c == '-') w = -1; c = getchar (); }
		while (isdigit (c)) x = (x << 3) + (x << 1) + (c ^ 48), c = getchar ();
		return x * w;
	}
	inline void In () {
		m = rnt (), n = rnt ();
		_for (i, 1, n) {
			scanf ("%s", s + 1);
			ac.Insert (s, i);
		}
		return;
	}
	inline void Solve () {
		ac.Build ();
		ans = ac.BFS ((1 << n) - 1, m);
		if (ans <= 42) ac.DFS (0, 0, 0, (1 << n) - 1, m);
		return;
	}
	inline void Out () {
		printf ("%lld\n", ans);
		if (ans <= 42) ac.PrintAns (0, 0, 0, m);
		return;
	}
}

namespace MATRIX {
	class Matrix {
	private:
		ll n; ldb a[N][N];
	public:
		inline ldb* operator [] (ll x) { return a[x]; }
		inline void Init (ll nn) { n = nn, memset (a, 0, sizeof (a)); return; }
		inline Matrix operator * (Matrix another) const {
			Matrix ans; ans.Init (n);
			_for (i, 0, n) _for (j, 0, n) _for (k, 0, n)
				ans[i][j] += a[i][k] * another[k][j];
			return ans;
		}
		inline void Print () {
			printf ("%lld\n", n);
			_for (i, 0, n) { _for (j, 0, n) printf ("%Lf ", a[i][j]); puts (""); }
			puts ("");
			return;
		}
	};
}

namespace ACAUTOMATON {
	class ACAutomaton {
	private:
		ll cnt = 0, nxt[N][26], fail[N], end[N];
	public:
		inline void Insert (std::string s) {
			ll p = 0, len = s.length () - 1;
			_for (i, 0, len) {
				ll c = s[i] - 'a';
				if (!nxt[p][c]) nxt[p][c] = ++cnt;
				p = nxt[p][c];
			}
			end[p] = 1;
			return;
		}
		inline ll Build (ll alphabet) {
			std::queue <ll> q;
			_for (i, 0, alphabet - 1) if (nxt[0][i]) fail[nxt[0][i]] = 0, q.push (nxt[0][i]);
			while (!q.empty ()) {
				ll u = q.front (); q.pop ();
				_for (i, 0, alphabet - 1) {
					if (nxt[u][i]) fail[nxt[u][i]] = nxt[fail[u]][i], q.push (nxt[u][i]);
					else nxt[u][i] = nxt[fail[u]][i];
				}
				end[u] |= end[fail[u]];
			}
			return cnt;
		}
		inline MATRIX::Matrix GetMatrix (ll alphabet) {
			MATRIX::Matrix ma; ma.Init (cnt + 1);
			_for (i, 0, cnt) {
				_for (j, 0, alphabet - 1) {
					if (end[nxt[i][j]]) ma[i][0] += 1.0 / (ldb)(alphabet), ma[i][cnt + 1] += 1.0 / (ldb)(alphabet);
					else ma[i][nxt[i][j]] += 1.0 / (ldb)(alphabet);
				}
			}
			ma[cnt + 1][cnt + 1] = 1.0;
			return ma;
		}
	};
}

namespace SOLVE {
	ll n, m, len, alphabet;
	std::string s[N];
	MATRIX::Matrix ans;
	ACAUTOMATON::ACAutomaton ac;
	inline ll rnt () {
		ll x = 0, w = 1; char c = getchar ();
		while (!isdigit (c)) { if (c == '-') w = -1; c = getchar (); }
		while (isdigit (c)) x = (x << 3) + (x << 1) + (c ^ 48), c = getchar ();
		return x * w;
	}

	inline MATRIX::Matrix FastPow (MATRIX::Matrix a, ll b) {
		MATRIX::Matrix an; an.Init (m);
		_for (i, 0, m) an[i][i] = 1.0;
		while (b) {
			if (b & 1) an = an * a;
			a = a * a, b >>= 1;
		}
		return an;
	}

	inline void In () {
		n = rnt (), len = rnt (), alphabet = rnt ();
		_for (i, 1, n) {
			std::cin >> s[i];
			ac.Insert (s[i]);
		}
		return;
	}
	inline void Solve () {
		m = ac.Build (alphabet) + 1;
		MATRIX::Matrix ma = ac.GetMatrix (alphabet);
		ans.Init (m), ans[0][0] = 1.0;
		ma = FastPow (ma, len), ans = ans * ma;
		return;
	}
	inline void Out () {
		printf ("%.10Lf\n", ans[0][m]);
		return;
	}
}