function decodeOrder(xs) {
    var rem = [...xs].sort(), code = 0n;
    xs.forEach((x, i) => {
        var j = rem.indexOf(x);
        code = code * BigInt(xs.length - i) + BigInt(j);
        rem.splice(j, 1);
    });
    return code;
}

function decodeOrderStr(xs) {
    for (var chars = [], n = decodeOrder(xs); n; n >>= 8n)
        chars.push(String.fromCharCode(Number(n & 255n)));
    return chars.reverse().join("");
}


/// All-in-one version.

function decodeOrderStrCombined(xs) {
    var rem = [...xs].sort(), n = 0n;
    xs.forEach((x, i) => {
        var j = rem.indexOf(x);
        n = n * BigInt(xs.length - i) + BigInt(j);
        rem.splice(j, 1);
    });

    for (var chars = []; n; n >>= 8n)
        chars.push(String.fromCharCode(Number(n & 255n)));
    return chars.reverse().join("");
}


/// Only needed for encoding.

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

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

  for (var 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;
}

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