Many people love numbers, and some have a penchant for specific numbers. Nowadays in popular culture, 1145141919 is a very fragrant number, and many people want to represent all other numbers with this number.
Let S be an infinite string of "1145141919" infinitely stitched together as "114514191911451419191145141919...".
Take a prefix T of S , you can insert '( ' , ') ' , '+ ' or '∗ ' to T to form a new string T′ , and then let the value of T′ be val(T′) according to ordinary rules. (You can insert any number of operators, even 0. But need to ensure that the inserted operators form legitimate operations)
Now for a number N , please calculate the minimum length of T that can make val(T′)=N . For example, when N=520 , the minimum length of 6 (pick the first 6 characters 114514 and insert operators to make T′=1+1+4+514 , then we have val(T′)=520 )
If no such T exists, output −1 .