题目描述
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 ($1 \leq N \leq 10^9$). 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
Output the minimized number of the replaced characters. If there is no way to replace, output $-1$ instead.
Examples
Input
100
+123
Output
2
Input
10
+123
Output
4
Input
1
+123
Output
-1
Input
10
++1+
Output
2
Input
2000
1234++7890
Output
2
输入格式
见题面
输出格式
见题面