Problem 104: Aliens Multiply Rapidly

(U.M. ACM Runoffs 2001, problem 4)

Description

It is generally believed that the best way to communicate with aliens if we ever come across any will be with the language of mathematics. Senator Cletus S. J. Yokell (Rep., Georgia), not quite understanding the idea, has decided that we must not look bad in front of the Martians by being slow in our calculations. To ensure this, he has appropriated a shit-load of money from congress to fund the construction of an alien-compatible calculator.

As we have never met a Martian, we don't know how many fingers they've got, and therefore we don't know what base they will represent numbers in. However, the senator is certain that Martians will not be superior to us, so we are guaranteed the base will not be more than 10.

You must write a program that can perform arithmetical calulations in any base (between 2 and 10 inclusive).

Input Format

The input will contain a number of test cases, each occupying two lines. The first line of each case will be the base, B, written as a normal decimal integer. A value of zero for B indicates the end of the input, and should not be processed.
The second line of each case will be an expression involving base-B numbers and the operators +, -, *, and /. There will be no other symbols, not even spaces, on the line. Operations should be performed in strictly left-to-right order, there are no "priorities" attached to operators.

Output Format

For each test case, print out the value of the expression, in base-B, alone on a single line.

Limits

You are assured that no calculation (intermediate results included) will produce a result greater than 1,000,000,000 (decimal) or less than zero. Nobody will ever try to divide by zero, and no division will ever produce a result that is not an exact integer.

Sample Input

10
123+456+1
2
11111*1000+11
10
2+3*4
5
12*40
0

Sample Output