#include "bits/stdc++.h" using namespace std; #define FOR(i,j,k) for(int (i)=(j);(i)<(int)(k);++(i)) #define rep(i,j) FOR(i,0,j) #define each(x,y) for(auto &(x):(y)) #define mp make_pair #define mt make_tuple #define all(x) (x).begin(),(x).end() #define debug(x) cout<<#x<<": "<<(x)< pii; typedef vector vi; typedef vector vll; /*** 誤差関数 erf(x) = 2/sqrt(PI) *∫(0<=t<=x, e^(-t^2))dt 標準正規分布の確率 P(0<=X<=a) = ∫(0<=x<=a, 1/sqrt(2*PI)*e^(-x^2/2))dx = ∫(0<=t<=sqrt(2)/2 * a, 1/sqrt(2*PI)*e^-t^2*sqrt(2))dt = 1/2 * { 2/sqrt(PI) * ∫(0<=t<=sqrt(2)/2 * a, e^(-t)^2)dt } = 1/2 * erf(sqrt(2)/2*a) (x1+x2+...xn)/n がx 以下 になる確率 ***/ double centralLimitTheorem(long long n, double x, double mean, double sd) { double y = (x - mean) / sd * sqrt(2.0 * n) / 2; double res = 0; if(y < 0) res = 0.5 * (1 - erf(-y)); else res = 0.5 * (1 + erf(y)); return res; } double dp[2][12001]; double f(int N, int L, int R) { double p = 1 / 6.0; dp[0][0] = 1; rep(i, N) { int c = i & 1; fill_n(dp[!c], (i + 1) * 6 + 1, 0.0); rep(j, i * 6 + 1) { for(int k = 1; k <= 6; ++k) { dp[!c][j + k] += dp[c][j] * p; } } } double ans = 0; for(int i = L; i <= R; ++i) { ans += dp[N&1][i]; } return ans; } int main() { ios::sync_with_stdio(false); cin.tie(0); ll N, L, R; double m = 3.5; double sd = sqrt(35.0 / 12); while(cin >> N >> L >> R) { smin(L, N * 6); smin(R, N * 6); smax(L, N); if(N > 2000) { double l = L ? centralLimitTheorem(N, (double)(L-0.5) / N, m, sd) : 0; double r = R ? centralLimitTheorem(N, (double)(R+0.5) / N, m, sd) : 0; double ans = r - l; cout << setprecision(20) << ans << endl; } else { cout << setprecision(20) << f(N, L, R) << endl; } } }