Time Limit : 2 sec, Memory Limit : 524288 KB

Problem G. Additions

You are given an integer $N$ and a string consisting of '+' and digits. You are asked to transform the string into a valid formula whose calculation result is smaller than or equal to $N$ by modifying some characters. Here, you replace one character with another character any number of times, and the converted string should still consist of '+' and digits. Note that leading zeros and unary positive are prohibited.

For instance, '0123+456' is assumed as invalid because leading zero is prohibited. Similarly, '+1+2' and '2++3' are also invalid as they each contain a unary expression. On the other hand, '12345', '0+1+2' and '1234+0+0' are all valid.

Your task is to find the minimum number of the replaced characters. If there is no way to make a valid formula smaller than or equal to $N$, output $-1$ instead of the number of the replaced characters.


The input consists of a single test case in the following format.


The first line contains an integer $N$, which is the upper limit of the formula ($1 \leq N \leq 10^9$). The second line contains a string $S$, which consists of '+' and digits and whose length is between $1$ and $1,000$, inclusive. Note that it is not guaranteed that initially $S$ is a valid formula.


Output the minimized number of the replaced characters. If there is no way to replace, output $-1$ instead.


Sample Input 1


Output for Sample Input 1


Sample Input 2


Output for Sample Input 2


Sample Input 3


Output for Sample Input 3


Sample Input 4


Output for Sample Input 4


Sample Input 5


Output for Sample Input 5


In the first example, you can modify the first two characters and make a formula '1+23', for instance. In the second example, you should make '0+10' or '10+0' by replacing all the characters. In the third example, you cannot make any valid formula less than or equal to $1$.