function facts(n) {
  const f = [1n];
  for (let i = 1; i <= n; i++) f[i] = f[i - 1] * BigInt(i);
  return f;
}

function decodeOrder(xs) {
  const rem = [...xs].sort(), f = facts(xs.length);
  let code = 0n;

  for (let i = 0; i < xs.length; i++) {
    const j = rem.indexOf(xs[i]);
    if (j < 0) throw Error("duplicate item");
    code += BigInt(j) * f[xs.length - 1 - i];
    rem.splice(j, 1);
  }

  return code;
}

function encodeOrder(xs, code) {
  const rem = [...xs].sort(), out = [], f = facts(xs.length);
  code = BigInt(code);

  for (let i = xs.length; i > 0; i--) {
    const q = code / f[i - 1];
    code %= f[i - 1];
    out.push(rem.splice(Number(q), 1)[0]);
  }

  return out;
}

/// Extras

function strToBignum(s) {
    return [...s].reduce((n, c) => (n << 8n) | BigInt(c.charCodeAt(0)), 0n);
}

function bignumToStr(n) {
    let s = "";
    for (n = BigInt(n); n; n >>= 8n) {
        s = String.fromCharCode(Number(n & 255n)) + s;
    }
    return s;
};

function encodeOrderStr(xs, s) {
    return encodeOrder(xs, strToBignum(s));
}

function decodeOrderStr(xs) {
    return bignumToStr(decodeOrder(xs));
}