var input, current, index;

var _OPERATOR = 1;
var _NUMBER = 2;
var _EOF = 3;

function next() {
  var char, token = {};

  while(index < input.length) {
    char = input.charAt(index++);
    switch(char) {
      case '+':
      case '-':
      case '*':
      case '/':
      case '(':
      case ')':
    token.operator = char;
    token.type = _OPERATOR;
    return token;

      case '0':
      case '1':
      case '2':
      case '3':
      case '4':
      case '5':
      case '6':
      case '7':
      case '8':
      case '9':
    token.value = char;
    token.type = _NUMBER;
    return token;

      default:
    throw "Unexpected character: " + c;
    }
  }
  token.type = _EOF;
  return token;
}


function peek() {
  if(!current)
    current = next();

  return current;
}

function skip() {
  if(!current)
    current = next();
  current = undefined;
}

function parseString(str) {
  input = str;
  index = 0;

  return tree();
}


function tree() {
  return add();
}

function add() {
  var left = multDivide();
    var token = peek();
    while(token.type == _OPERATOR && (token.operator == '+' || token.operator == '-') ) {
        skip();
        var node = {};
        node.operator = token.operator;
        node.left = left;
        node.right = multDivide();
        left = node;
    token = peek();
    }
    return left;
}

function multDivide() {
  var left = root();
    var token = peek();
    while(token.type == _OPERATOR &&  (token.operator == '*' || token.operator == '/') ) {
        skip();
        var node = {};
        node.operator = token.operator;
        node.left = left;
        node.right = root();
        left = node;
    token = peek();
    }
    return left;
}

function root() {
  var token = peek();
  if(token.type == _NUMBER) {
    skip();
    node = {};
    node.value = token.value;
    return node;
  }
  
}