#[allow(unused_imports)] use std::cmp::*; #[allow(unused_imports)] use std::collections::*; use std::io::*; #[allow(dead_code)] fn getline() -> String { let mut ret = String::new(); std::io::stdin().read_line(&mut ret).ok(); return ret; } fn get_word() -> String { let mut stdin = std::io::stdin(); let mut u8b: [u8; 1] = [0]; loop { let mut buf: Vec = Vec::with_capacity(16); loop { let res = stdin.read(&mut u8b); if res.is_err() || res.ok().unwrap() == 0 || u8b[0] <= ' ' as u8 { break; } else { buf.push(u8b[0]); } } if buf.len() >= 1 { let ret = std::string::String::from_utf8(buf).unwrap(); return ret; } } } fn parse(s: &str) -> T { s.parse::().ok().unwrap() } #[allow(dead_code)] fn get() -> T { parse(&get_word()) } fn main() { let n = 80 - get::(); let p0: f64 = get::() / 100.0; let p1: f64 = get::() / 100.0; let p2: f64 = get::() / 100.0; const B: usize = 14; let mut decay = vec![vec![0.0; B]; 1 << B]; for bits in 0 .. 1 << B { for j in 0 .. B { if (bits & 1 << j) == 0 { continue; } let p; let mut adj = 0; if j == 0 || (j >= 1 && (bits & 1 << (j - 1)) == 0) { adj += 1; } if j == B - 1 || (j < B - 1 && (bits & 1 << (j + 1)) == 0) { adj += 1; } p = match adj { 0 => p2, 1 => p1, 2 => p0, _ => panic!(), } + 1e-8; decay[bits][j] = p; } } let mut dp = vec![vec![0.0; 1 << B]; n + 1]; dp[0][(1 << B) - 1] = 1.0; for i in 0 .. n { for b1 in 0 .. 1 << B { let mut b2 = b1; let mut prob = 1.0; for j in 0 .. B { if (b1 & 1 << j) == 0 { continue; } prob *= 1.0 - decay[b1][j]; } loop { /* for j in 0 .. B { if (b1 & 1 << j) == 0 { continue; } let p = decay[b1][j]; prob *= if (b2 & 1 << j) == 0 { p } else { 1.0 - p }; } */ dp[i + 1][b2] += prob * dp[i][b1]; if b2 == 0 { break; } let newb2 = (b2 - 1) & b1; for j in 0 .. B { if (b1 & 1 << j) == 0 { continue; } if (b2 & 1 << j) == (newb2 & 1 << j) { break; } if (newb2 & 1 << j) == 0 { prob *= decay[b1][j] / (1.0 - decay[b1][j]); } else { prob *= (1.0 - decay[b1][j]) / decay[b1][j]; } } b2 = newb2; } } } let mut tot = 0.0; for i in 0 .. 1 << B { tot += ((i as u32).count_ones() as f64) * dp[n][i]; } println!("{}", 2.0 * tot); }