How Many Zeros?

Time limit1sMemory limit128 MB

Summary

For each range n to m, count how many times the digit 0 appears when every integer in the range is written in decimal without leading zeros.

Level: Medium7 of 10
Topics: Math, Implementation, Number theory, Brute force
Solved: No attempts yet

Problem

Write a program that, when every integer from $n$ to $m$ is written down one by one on paper, counts how many times the digit $0$ is written. Each number is written in decimal with no leading zeros. For example, writing $10$ writes the digit $0$ once, and the number $0$ is written as " $0$ ", which is one zero.

Input

The input consists of several test cases. Each test case is a single line containing two integers $n$ and $m$ separated by a space, with $n \le m$ . On the last line $n$ is negative; do not process that line and terminate the program.

Output

For each test case, print on its own line the total number of times the digit $0$ is written when listing the numbers from $n$ to $m$ .

Examples6

Example 1

Input

10 11
100 200
0 500
1234567890 2345678901
0 4294967295
-1 -1

Expected output

Example 2
Input
```
0 0
-1 -1
```
Expected output
```
1
```
Example 3
Input
```
1 9
-1 -1
```
Expected output
```
0
```
Example 4
Input
```
5 15
-1 -1
```
Expected output
```
1
```
Example 5
Input
```
100 100
-1 -1
```
Expected output
```
2
```
Example 6
Input
```
0 1
-1 -1
```
Expected output
```
1
```