function generateParenthesis(n) {
  const output = []
  const rec = (input = [], left = 0, right = 0) => {
    if (input.length === 2*n) {
      output.push(input.join(''));
      console.log('sol');
      return
    }
    if (left < n) {
      input.push('(');
      console.log(input.join('') + ' l=' + left + ' r=' + right)
      rec(input, left+1, right);
      console.log('back left');
      input.pop();
    }

    if (right < left) {
      input.push(')');
      console.log(input.join('') + ' l=' + left + ' r=' + right)
      rec(input, left, right+1);
      console.log('back right l=' + left);
      input.pop();
      console.log(input.join('') + ' l=' + left + ' r=' + right)
    }
  };
  rec();
  return output;
}

console.log(generateParenthesis(3));