Cryptogram#7199

Cryptogram

1 second
64 megabytes
Very hard

Create a program that deciphers an addition expression where all addends are separated by the sign, and the sum is preceded by the sign. The expression is encoded such that:

Input

The first line contains a natural number representing the base of the numeral system, which ranges from to inclusive. The second line contains the encoded addition expression. There are no additional spaces separating the addends, the sum, or the and signs.

Output

Output all possible ways to decipher the given addition expression, with each solution on a new line and without repetition. The order of the solutions does not matter.

Examples

Example 1

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