Rikka is a professional problem setter. Today, she is going to generate test cases for a problem about Composite Number.
To randomly generate composite numbers, Rikka starts from a non-empty subset D of digits and integer c = 0, and then generates in turns. In each turn:
The time cost of a generator is crucial. Therefore, Rikka wants you to calculate the expected number of the turns used by the generator to generate a composite number.
A positive integer n is a composite integer if and only if there exists an integer satisfying k is a factor of n.

The first line contains a 01-string of length 9. The i-th character is 1 if and only if digit i is inside D.
The input guarantees that D is not empty.

Output a single integer, representing the expected number of turns.
The answer is guaranteed to be a rational number. You are required to output the answer module 998244353. Formally, if the simplest fraction representation of the answer is , you need to output .

100000000

3

The generator must return 111 in the third turn.

001100000

499122178

There are 3 possibilities:
1. Return 4 in the first turn, with probability .
2. Return 33 in the second turn, with probability .
3. Return 34 in the second turn, with probability .
Therefore, the expected number of turns is .