Time Limit: 2 sec / Memory Limit: 512 MB

### Problem Statement

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.

### Input

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

$N$ $S$

The first line contains an integer $N$, which is the upper limit of the formula ($1 \le N \le 10^9$). 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

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

### Sample Input 1

100 +123

### Output for Sample Input 1

2

### Sample Input 2

10 +123

### Output for Sample Input 2

4

### Sample Input 3

1 +123

### Output for Sample Input 3

-1

### Sample Input 4

10 ++1+

### Output for Sample Input 4

2

### Sample Input 5

2000 1234++7890

### Output for Sample Input 5

2

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 $1$.