// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;

fn main() {
    input! {
        n: usize, m: usize,
        mut e: [(Usize1, Usize1); m]
    }
    e.sort();
    let mut tree = vec![vec![]; n];
    for &(s, t) in &e {
        tree[s].push(t);
    }

    fn dfs(memo: &mut [(f64, Vec<f64>)], tree: &[Vec<usize>], i: usize) {
        if i == memo.len() - 1 {
            return;
        }
        let mut s = 0.;
        let mut v = vec![];
        for &t in &tree[i] {
            if memo[t].0 < 0. {
                dfs(memo, tree, t);
            }
            let x = memo[t].0 + 1.;
            v.push(x);
            s += x;
        }

        let res = s as f64 / tree[i].len() as f64;
        memo[i].0 = res;
        memo[i].1 = v;
    }
    let mut memo = vec![(-1., vec![]); n];
    memo[n - 1].0 = 0.;
    dfs(&mut memo, &tree, 0);

    let mut v_rate = vec![0.; n];
    v_rate[0] = 1.0f64;
    let mut res = memo[0].0;
    for i in 0..n {
        if tree[i].len() == 1 {
            v_rate[tree[i][0]] += v_rate[i];
            continue;
        }
        if tree[i].len() != memo[i].1.len() {
            continue;
        }

        for j in 0..tree[i].len() {
            v_rate[tree[i][j]] += v_rate[i] / tree[i].len() as f64;
            let x = (memo[i].0 * (tree[i].len() as f64) - (memo[i].1)[j])
                / ((tree[i].len() - 1) as f64);
            res = res.min(memo[0].0 - (memo[i].0 - x) * v_rate[i]);
        }
    }
    println!("{}", res);
}
*/

fn main() {
    let exe = "/tmp/bin826FEE17";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "
f0VMRgIBAQAAAAAAAAAAAAIAPgABAAAAYANAAAAAAABAAAAAAAAAAHDyAwAAAAAAAAAAAEAAOAAHAEAA
EAAPAAEAAAAFAAAAAAAAAAAAAAAAAEAAAAAAAAAAQAAAAAAACMkDAAAAAAAIyQMAAAAAAAAAIAAAAAAA
AQAAAAYAAAAg1wMAAAAAACDXYwAAAAAAINdjAAAAAAC4GgAAAAAAAAg2AAAAAAAAAAAgAAAAAAAEAAAA
BAAAAMgBAAAAAAAAyAFAAAAAAADIAUAAAAAAACQAAAAAAAAAJAAAAAAAAAAEAAAAAAAAAAcAAAAEAAAA
INcDAAAAAAAg12MAAAAAACDXYwAAAAAAMAAAAAAAAADIAAAAAAAAACAAAAAAAAAAUOV0ZAQAAADMgAMA
AAAAAMyAQwAAAAAAzIBDAAAAAAAsCgAAAAAAACwKAAAAAAAABAAAAAAAAABR5XRkBgAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAQAAAAAAAAAFLldGQEAAAAINcDAAAAAAAg12MA
AAAAACDXYwAAAAAA4BgAAAAAAADgGAAAAAAAAAEAAAAAAAAABAAAABQAAAADAAAAR05VAM9Ih6Mq9kXo
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";


Measured memory_bytes: 13268