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Unknown Language Round #3:

- Pike 7.8

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F. Polynom

time limit per test

2 secondsmemory limit per test

64 megabytesinput

standard inputoutput

standard outputYou 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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