Some positive integers can be represented by a sum of one or more consecutive prime numbers. How many such representations does a given positive integer have? 
For example, the integer 53 has two representations $5 + 7 + 11 + 13 + 17$ and $53$. The integer $41$ has three representations $2+3+5+7+11+13, 11+13+17$, and $41$. The integer $3$ has only one representation, which is $3$. The integer $20$ has no such representations. Note that summands must be consecutive prime numbers, so neither $7 + 13$ nor $3 + 5 + 5 + 7$ is a valid representation for the integer $20$.
Your mission is to write a program that reports the number of representations for the given positive integer.

The input is a sequence of positive integers each in a separate line. The integers are between $2$ and $10,000$, inclusive. The end of the input is indicated by a zero.

The output should be composed of lines each corresponding to an input line except the last zero. An output line includes the number of representations for the input integer as the sum of one or more consecutive prime numbers. No other characters should be inserted in the output.