Divisibility by 4#2423

Divisibility by 4

1 second

64 megabytes

Easy

Let us consider an infinite sequence of numbers constructed as follows:

$A_{0} = 1, A_{1} = 12, \dots, A_{9} = 12345678910, A_{10} = 1234567891011, \dots$ A_0 = 1, A_1 = 12, \ldots, A_9 = 12345678910, A_{10} = 1234567891011, \ldots

That is, each next term in the sequence is obtained by appending to the previous term the decimal representation of the number that is one greater than the index of the current term.

You need to determine the total number of elements in the sequence within the index range $[m, n]$ ( $0 \leq m \leq n \leq 1 0^{18}$ 0 \le m \le n \le 10^{18}) that are divisible by $4$ without a remainder.

Input

The only line of input contains two non-negative integers $m$ and $n$ .

Output

Print a single integer — the answer to the problem.

Examples

Example 1

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A_{0} = 1, A_{1} = 12, \dots, A_{9} = 12345678910, A_{10} = 1234567891011, \dots

0 \leq m \leq n \leq 1 0^{18}