function Stack() {
  this.dataStore = [];
  this.top = 0;
  this.push = push;
  this.pop = pop;
  this.peek = peek;
  this.length = length;
}

function push(element) {
  this.dataStore[this.top++] = element;
}

function pop() {
  return this.dataStore[--this.top];
}

function peek() {
  return this.dataStore[this.top-1];
}

function length() {
  return this.top;
}

var infix = "3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3";
infix = infix.replace(/\s+/g, ''); // remove spaces, so infix[i]!=" "

var s = new Stack();
var ops = "-+/*^";
var precedence = {"^":4, "*":3, "/":3, "+":2, "-":2};
var associativity = {"^":"Right", "*":"Left", "/":"Left", "+":"Left", "-":"Left"};
var token;
var postfix = "";
var o1, o2;

for (var i = 0; i < infix.length; i++) {
  token = infix[i];
  if (token >= "0" && token <= "9") { // if token is operand (here limited to 0 <= x <= 9)
    postfix += token + " ";
  }
  else if (ops.indexOf(token) != -1) { // if token is an operator
    o1 = token;
    o2 = s.peek();
    while (ops.indexOf(o2)!=-1 && ( // while operator token, o2, on top of the stack
      // and o1 is left-associative and its precedence is less than or equal to that of o2
      (associativity[o1] == "Left" && (precedence[o1] <= precedence[o2]) ) ||
      // the algorithm on wikipedia says: or o1 precedence < o2 precedence, but I think it should be
      // or o1 is right-associative and its precedence is less than that of o2
      (associativity[o1] == "Right" && (precedence[o1] < precedence[o2]))
      )){
        postfix += o2 + " "; // add o2 to output queue
        s.pop(); // pop o2 of the stack
        o2 = s.peek(); // next round
    }
    s.push(o1); // push o1 onto the stack
  }
  else if (token == "(") { // if token is left parenthesis
    s.push(token); // then push it onto the stack
  }
  else if (token == ")") { // if token is right parenthesis
    while (s.peek() != "("){ // until token at top is (
      postfix += s.pop() + " ";
    }
    s.pop(); // pop (, but not onto the output queue
  }
}
postfix += s.dataStore.reverse().join(" ");
print(postfix);