We say that ** X** is a

**subnumber**of

**if**

`N`**can be obtained from**

`X`**by removing some (possibly none) of its digits.**

`N`For instance, the subnumbers of

**are**

`423`**, while the subnumbers of**

`[2, 3, 4, 23, 42, 43, 423]`**are**

`777`**.**

`[7, 77, 777]`A number is special if all of its subnumbers are prime. Given an interval ** [a, b]**, find how many special numbers it contains.

### Input

Two space-separated integers: ** a** and

**.**

`b`### Output

A single integer: the number of special numbers in the interval ** [a, b]**.

### Constraints

`1 ≤ a ≤ b ≤ 10`^{9}is not a prime number.`1`

### Sample

Input | Output | Explanation |
---|---|---|

20 30 | 1 | The only special number contained in the interval is . 23 |

Let's analyze some properties of constructing special numbers:

- We can only use prime digits:
.`2, 3, 5, 7` - We can not use the same digit twice, as it would create a subnumber which is a multiple of
.`11` - If we use
or`2`, they must be the first digit in the number. Otherwise, at least one subnumber would be either even or a multiple of`5`.`5`

All of these constraints reduce the search space by a significant amount. From this point on, we can easily generate **all** special numbers: ** [2, 3, 5, 7, 23, 37, 53, 73]**.

The query constraint is what makes this problem tricky, as there is no special number in the interval ** [74, 10^{9}]**.