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/**
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 * @param {string} S
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 * @return {string}
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 */
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var makeLargestSpecial = function (S) {
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  let t = S;
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  while (true) {
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    let t1 = largest(t);
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    if (t1 == t) return t;
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    t = t1;
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  }
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  function largest(S) {
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    let arr = S.split("").map((x) => Number.parseInt(x)),
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      num = Number.parseInt(S, 2),
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      rtn = S;
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    for (let firstEndIndex = 1; firstEndIndex < S.length - 2; firstEndIndex++) {
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      for (let lLength = 2; lLength < firstEndIndex + 2; lLength += 2) {
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        let firstStartIndex = firstEndIndex - lLength + 1;
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        if (!isSpecial(firstStartIndex, firstEndIndex)) continue;
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        for (
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          let rLength = 2;
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          rLength < S.length - firstEndIndex;
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          rLength += 2
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        ) {
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          let secondStartIndex = firstEndIndex + 1,
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            secondEndIndex = firstEndIndex + rLength;
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          if (!isSpecial(secondStartIndex, secondEndIndex)) continue;
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          let str = [
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            ...arr.slice(0, firstStartIndex),
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            ...arr.slice(secondStartIndex, secondEndIndex + 1),
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            ...arr.slice(firstStartIndex, firstEndIndex + 1),
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            ...arr.slice(secondEndIndex + 1),
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          ].join("");
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          let newNum = Number.parseInt(str, 2);
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          if (newNum > num) {
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            num = newNum;
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            rtn = str;
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          }
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        }
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      }
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    }
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    return rtn;
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    function isSpecial(start, end) {
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      let t = 0;
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      for (let i = start; i <= end; i++) {
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        t += arr[i] == 1 ? 1 : -1;
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        if (t < 0) return false; // this is the second rule, really bad description
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      }
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      return t == 0 ? true : false;
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    }
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  }
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};
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// console.log(makeLargestSpecial("101101011000"))