#include <bits/stdc++.h>
using namespace std;
typedef __int128_t LL;

void write(LL x, char ed) {
	if (x >= 10) write(x / 10, 0);
	putchar(x % 10 + '0');
	if (ed) putchar(ed);
}

struct Frac {
	LL p, q;
	Frac() {}
	Frac(LL x, LL y) { LL g = __gcd(x, y); p = x / g, q = y / g; }
	Frac operator* (Frac y) {
		LL g = __gcd(q * y.q, p * y.p);
		return Frac(p * y.p / g, q * y.q / g);
	}
	Frac operator+ (Frac y) {
		LL g = __gcd(p * y.q + q * y.p, q * y.q);
		return Frac((p * y.q + q * y.p) / g, q * y.q / g);
	}
	bool operator< (Frac y) {
		return p * y.q < q * y.p; 
	}
	bool operator> (Frac y) {
		return y < (*this);
	}
	bool operator== (Frac y) {
		return !(((*this) < y) || (y < (*this)));
	}
	bool operator!= (Frac y) {
		return !((*this) == y);
	}
	void operator+= (Frac y) { (*this) = (*this) + y; }
	void operator*= (Frac y) { (*this) = (*this) * y; }
	double val() { if (q == 0) return 1e18; return (double)1. * p / q; }
};
Frac min(Frac x, Frac y) { return x < y ? x : y; }
Frac max(Frac x, Frac y) { return x > y ? x : y; }

LL n, T;
LL num[50005][2];

Frac dfs(vector<LL> now, int lev, Frac pro) {
	if (now.size() == 2) return Frac((now[0] > now[1]) + (now[0] >= now[1]), 2) * pro;
	LL mx = 0; vector<int> mxp;
	for (int i = 0; i < now.size(); i++) mx = max(mx, now[i]);
	for (int i = 0; i < now.size(); i++) if (now[i] == mx) mxp.push_back(i);
	Frac res(0, 1);
	if (mxp[0] == 0) {
		vector<LL> tmp; Frac mn(1, 0);
		map<LL, bool> mp;
		for (int i = 1; i < now.size(); i++) {
			if (mp[now[i]]) continue;
			vector<LL>().swap(tmp); mp[now[i]] = true;
			for (int j = 0; j < now.size(); j++) {
				if (j == 0) tmp.push_back(now[j] * (lev - 2));
				else if (j != i) tmp.push_back(now[j] * (lev - 1));
			}
			mn = min(mn, dfs(tmp, lev - 1, pro * Frac(1, mxp.size())));
		}
		res += mn;
	}
	if (mxp.size() > (mxp[0] == 0)) {
		vector<LL> tmp; Frac mn(1, 0); map<LL, bool> mp2;
		for (int i = mxp[(mxp[0] == 0)], j = 1; j < now.size(); j++) {
			if (i == j || mp2[now[j]]) continue;
			mp2[now[j]] = true;
			vector<LL>().swap(tmp);
			for (int k = 0; k < now.size(); k++) {
				if (k == i) tmp.push_back(now[k] * (lev - 2));
				else if (k != j) tmp.push_back(now[k] * (lev - 1));
			}
			mn = min(mn, dfs(tmp, lev - 1, pro * Frac(1, mxp.size())));
		}
		res += mn * Frac((mxp.size() - (mxp[0] == 0)), 1);
	}
//	if (lev >= 7) printf("%d %.6lf %.6lf\n", lev, pro.val(), res.val());
//	if (lev >= 7) { for (int i : now) cout << i << " "; cout << endl; }
	return res;
}

LL a, b;
void exgcd(LL x, LL y) {
	if (x == 1) { a = 1, b = 0; return; }
	exgcd(y % x, x);
	LL d = y / x, tmp = a;
	a = b - tmp * d, b = tmp;
}

LL solve() {
	LL now = 1, res = 0;
	for (int i = 1; i <= T; i++) {
		LL res1 = (num[i][0] - res), g = __gcd(now, num[i][1]);
		if (res1 < 0) swap(num[i][0], res), swap(num[i][1], now), res1 = -res1;
		if (res1 % g != 0) { printf("error\n"); exit(0); }
		LL res2 = res1 / g;
		a = 0, b = 0; exgcd(now / g, num[i][1] / g);
//		cout << a << " " << b << endl;
		LL pos = (a % (num[i][1] / g) * res2 % (num[i][1] / g) + num[i][1] / g) % (num[i][1] / g);
		res = res + pos * now;
//		write(res, '\n');
		now = now / g * num[i][1];
	}
	return res;
}

int main() {
//	freopen("ex_data2.in", "r", stdin);
	scanf("%d", &T);
	for (int i = 1; i <= T; i++) {
		scanf("%lld %lld", &num[i][0], &num[i][1]);
	}
	n = solve();
//	cout << n << endl;
	if (n < 2) return printf("error\n"), 0;
//	if (n >= 12) return printf("0.000000\n"), 0;//, (Frac(1, n - 2) + Frac(1, n)).val()), 0;
	vector<LL> tmp;
	for (int i = 1; i <= n; i++) tmp.push_back(1);
	printf("%.6lf", dfs(tmp, n, Frac(1, 1)).val());
}