private void findMiddle(String s) {
		ArrayList<Integer> operations = new ArrayList<Integer>();
		
		// compile the index of each operator
		for(int i = 0; i < s.length(); i++) {
			if( s.charAt(i) == OR || s.charAt(i) == AND || s.charAt(i) == IMPLY) {
				operations.add(i);
			}
		}
		
		// if there is only one operator, then just branch based off of that
		if(operations.size() == 1) {
			left = new Node(s.substring(0, operations.get(0)));
			right = new Node(s.substring(operations.get(0)+1));
			root = s.charAt(operations.get(0)) + "";
		} else {
			// go through each operator and check if it's the middle
			for(Integer i : operations) {
				if(isMiddle(s, i)) {
					left = new Node(s.substring(0, i));
					right = new Node(s.substring(i+1));
					root = s.charAt(i) + "";
					break;
				}
			}
		}
	}