Construct a DFA to recognize unsigned binary strings evenly divisible by $7.$

You may accept empty string $($it won$$t be tested$).$

Leading zeros have no meaning, such as octal, e$.$g$.(0101$ and $0000101$ are both the number $5)$

The last five should accept, all previous reject.

There is a corresponding test file p$4$test.txt:

$01$

$10$

$11$

$100$

$0101$

$110$

$1000$

$00001001$

$1010$

$01011$

$1100$

$001101$

$00001111$

$10000$

$00010001$

$10010$

$010011$

$10100$

$10101$

$0$

$0111$

$1110$

$010101$