The package for this problem was not updated by the problem writer or Codeforces administration after we've upgraded the judging servers. To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.

Unknown Language Round 3 |
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Finished |

The following languages are only available languages for the problems from the contest

Unknown Language Round 3:

- Pike 7.8

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F. Polynom

time limit per test

2 secondsmemory limit per test

64 megabytesinput

stdinoutput

stdoutYou are given a polynom in form *p*(*x*) = (*x* + *a*_{1})·(*x* + *a*_{2})·... (*x* + *a*_{n}). Write Pike program to print it in a standard form *p*(*x*) = *x*^{n} + *b*_{1}*x*^{n - 1} + ... + *b*_{n - 1}*x* + *b*_{n}. You should write each addend in form «C*X^K» (for example, 5*X^8).

Please, write the polynom in the shortest way, so you should skip unnecessary terms: some terms «C*X^K» should be reduced or even omitted. Look for the samples for clarification.

Input

The first line of the input contains *n* (1 ≤ *n* ≤ 9). The following *n* lines contain integer *a*_{i} ( - 10 ≤ *a*_{i} ≤ 10).

Output

Print the given polynom in a standard way. Note, that the answer in this problem response uniquely determined.

Examples

Input

2

-1

1

Output

X^2-1

Input

2

1

1

Output

X^2+2*X+1

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