function importPackage(pack) {
    for (var x in pack) {
        global[x] = pack[x];
    }
}







var exceptions = (function () {
    function MyException(message) { this.message = message }
    MyException.prototype = Error.prototype;
    MyException.prototype.name = "MyException";

    function MakeException(name) { this.name = name }
    MakeException.prototype = MyException.prototype;

    function exceptionFactory(name, newMess) {
        var result = function () {
            MyException.call(this, newMess.apply(null, arguments));
        }
        result.prototype = new MakeException(name);
        return result;
    }

    var OddClosingParenthesisException = exceptionFactory(
        "OddClosingParenthesisException",
        function (expr, ind) {
            return ("Odd closing bracket at position: " + ind + "\n" + expr);
        }
    );

    var MissingClosingParenthesisException = exceptionFactory(
        "MissingClosingParenthesisException",
        function (expr, ind) {
            return ("Expected closing bracket before position: " + ind + "\n" + expr);
        }
    );

    var MissingOpeationParenthesisException = exceptionFactory(
        "MissingOpeationParenthesisException",
        function (expr, op, ind, mode) {
            var ending = op + "' at position: " + ind + "\n" + expr;
            if (!mode) {
                return ("Opening bracket expected before operation '" + ending);
            } else {
                return ("Closing bracket expected after operation '" + ending);
            }
        }
    );

    var MissingOperandException = exceptionFactory(
        "MissingOperandException",
        function (expr, op, ind) {
            return ("Overflow operands for operation '" + op + "' at position: " + ind + "\n" + expr );
        }
    );

    var OddOperandException = exceptionFactory(
        "OddOperandException",
        function (expr, op, ind) {
            return ("Too many operands for operation '" + op + "' at position: " + ind + "\n" + expr);
        }
    );

    var UnknownIdentifierException = exceptionFactory(
        "UnknownIdentifierException",
        function (expr, id, ind) {
            return ("Unknown identifier '" + id + "' at position: " + ind + "\n" + expr);
        }
    );

    var UnknownSymbolException = exceptionFactory(
        "UnknownSymbolException",
        function (expr, ind) {
            return ("Unknown symbol '" + expr.charAt(ind) + "' at position: " + ind + "\n" + expr);
        }
    );

    var MissingOperationException = exceptionFactory(
        "MissingOperationException",
        function (expr, ind, where) {
            var reason = "";
            if (!where) {
                reason = "Expected operation after opening bracket at position ";
            } else {
                reason = "Expected operation before closing bracket at position ";
            }
            return (reason + ind + "\n" + expr);
        }
    );

    var OddSuffixException = exceptionFactory(
        "OddSuffixException",
        function (expr, ind) {
            return ("Unexpected suffix after correct expression at position: " + ind  + "\n" + expr);
        }
    );

    return {
        "MyException": MyException,
        "OddClosingParenthesisException": OddClosingParenthesisException,
        "MissingClosingParenthesisException": MissingClosingParenthesisException,
        "MissingOperandException": MissingOperandException,
        "UnknownIdentifierException": UnknownIdentifierException,
        "UnknownSymbolException": UnknownSymbolException,
        "MissingOperationException": MissingOperationException,
        "OddSuffixException": OddSuffixException,
        "OddOperandException": OddOperandException,
        "MissingOpeationParenthesisException": MissingOpeationParenthesisException
    }
})();






var expression = (function () {
    importPackage(exceptions);

    function myNew(constructor, args) {
        var tmp = Object.create(constructor.prototype);
        constructor.apply(tmp, args);
        return tmp;
    }

    var VARIABLES = {"x": 0, "y": 1, "z": 2};
    function Const(x) {
        this.getValue = function () { return x }
    }
    Const.prototype.toString = function () { return this.getValue().toString() }
    Const.prototype.prefix = Const.prototype.toString;
    Const.prototype.evaluate = function () { return this.getValue() }

    function Variable(s) {
        var ind = VARIABLES[s];
        this.getName = function () { return s }
        this.getInd = function () { return ind }
    }

    Variable.prototype.toString = function () { return this.getName() }
    Variable.prototype.prefix = Variable.prototype.toString;
    Variable.prototype.evaluate = function () { return arguments[this.getInd()] }

    function Operation() {
        var operands = [].slice.call(arguments);
        this.getOperands = function () { return operands }
    }
    Operation.prototype.toString = function () {
        return this.getOperands().join(" ") + " " + this.getSymbol();
    }
    Operation.prototype.prefix = function () {
        return "(" +  this.getSymbol() + " " + this.getOperands().map(function (value) { return value.prefix() }).join(" ") + ")";
    }
    Operation.prototype.evaluate = function () {
        var args = arguments;
        var res = this.getOperands().map(function(value) { return value.evaluate.apply(value, args) });
        return this._action.apply(null, res);
    }

    function flag(a) {
        return (a instanceof Const || a instanceof Variable || a instanceof Operation);
    }

    function DefineOperation(action, symbol) {
        this._action = action;
        this.getSymbol = function () {
            return symbol;
        }
    }
    DefineOperation.prototype = Operation.prototype;

    function operationFactory(action, symbol) {
        var result = function () {
            var args = arguments;
            Operation.apply(this, args);
        }
        result.prototype = new DefineOperation(action, symbol);
        return result;
    }

    var Add = operationFactory(
        function (a, b) { return a + b },
        "+"
    );

    var Subtract = operationFactory(
        function (a, b) { return a - b },
        "-"
    );

    var Multiply = operationFactory(
        function (a, b) { return a * b },
        "*"
    );

    var Divide = operationFactory(
        function (a, b) { return a / b },
        "/"
    );

    var Negate = operationFactory(
        function (a) { return -a },
        "negate"
    );

    var ArcTan = operationFactory(
        function (a) { return Math.atan(a) },
        "atan"
    );

    var Exp = operationFactory(
        function (a) {return Math.exp(a) },
        "exp"
    );

    var OP = {
        "+": Add,
        "-": Subtract,
        "*": Multiply,
        "/": Divide,
        "negate": Negate,
        "atan": ArcTan,
        "exp": Exp
    };
    var ARGS_COUNT = {
        "+": 2,
        "-": 2,
        "*": 2,
        "/": 2,
        "negate": 1,
        "atan": 1,
        "exp": 1
    };

    var expr = "";
    var ind = 0;
    var stack = [];
    var index = [];

    function skipWhiteSpace() {
        while (ind < expr.length && /\s/.test(expr.charAt(ind))) {
            ind++;
        }
    }


    function parsePrefix(s) {
        var balance = 0;
        ind = 0;
        expr = s;
        stack = [];
        skipWhiteSpace();
        if (ind === expr.length) {
            throw new MyException("Empty input");
        }
        var mode = 0;
        while (true) {
            skipWhiteSpace();
            if (ind >= expr.length) {
                break;
            }
            if (expr.charAt(ind) === ")") {
                balance--;
                if (balance < 0) {
                    throw new OddClosingParenthesisException(expr, ind);
                }

                var tempInd = undefined;
                var curOperation = undefined;
                var operands = [];
                while ((stack[stack.length - 1] !== "(") && !(stack[stack.length - 1] in OP)) {
                    operands.push(stack.pop());
                    index.pop();
                }
                if (stack[stack.length - 1] === "(") {
                    throw new MissingOperationException(expr, index.pop(), mode);
                }
                curOperation = stack.pop();
                tempInd = index.pop();
                if (stack.pop() !== "(") {
                    throw new MissingOpeationParenthesisException(expr, curOperation, index.pop(), mode);
                }
                index.pop()
                if (operands.length > ARGS_COUNT[curOperation]) {
                    throw new OddOperandException(expr, curOperation, tempInd);
                } else if (operands.length < ARGS_COUNT[curOperation]) {
                    throw new MissingOperandException(expr, curOperation, tempInd);
                } else {
                    stack.push(myNew(OP[curOperation], operands.reverse()));
                }

                ind++;
                if (balance === 0) {
                    break;
                }
                continue;
            }
            index.push(ind);
            if (expr.charAt(ind) === "(") {
                stack.push("(");
                ind++;
                balance++;
                continue;
            }

            var curNumber = "";

            if (expr.charAt(ind) === "-") {
                curNumber += "-";
                ind++;
            }
            while (ind < expr.length && /\d/.test(expr.charAt(ind))) {
                curNumber += expr.charAt(ind++);
            }

            if (curNumber !== "" && curNumber !== "-") {
                stack.push(new Const(parseInt(curNumber)));
                continue;
            } else {
                if (curNumber === "-") {
                    ind--;
                }
            }
            var curOp = undefined;
            var curId;
            if (expr.charAt(ind) in OP) {
                curOp = expr.charAt(ind);
                ind++;
            } else {
                curId = "";

                if (!(/[A-Za-z]/.test(expr.charAt(ind)))) {
                    throw new UnknownSymbolException(expr, ind);
                }
                while (ind < expr.length && /\w/.test(expr.charAt(ind))) {
                    curId += expr.charAt(ind++);
                }

                if (curId in OP) {
                    curOp = curId;
                }
            }
            if (curOp !== undefined) {
                stack.push(curOp);
            } else if (curId in VARIABLES) {
                stack.push(new Variable(curId));
                if (balance === 0) {
                    break;
                }
            } else {
                throw new UnknownIdentifierException(expr, curId, index.pop());
            }
        }
        skipWhiteSpace();
        if (ind !== expr.length) {
            throw new OddSuffixException(expr, ind);
        } else if (balance > 0) {
            throw new MissingClosingParenthesisException(expr, ind);
        } else if (stack.length > 1) {
            throw new MissingOpeationParenthesisException(expr, stack[0], index[0], mode);
        }
        var res = stack.pop();
        if (!flag(res)) {
            throw new MissingOpeationParenthesisException(expr, res, index.pop(), mode);
        }
        return res;
    }

    return {
        "Const": Const,
        "Variable": Variable,
        "Add": Add,
        "Subtract": Subtract,
        "Multiply": Multiply,
        "Divide": Divide,
        "Negate": Negate,
        "parsePrefix": parsePrefix,
        "ArcTan": ArcTan,
        "Exp": Exp
    }

})();










importPackage(expression);