Ordinal Number

시간 제한2초메모리 제한2048 MB

요약

폰 노이만 순서수를 중괄호와 쉼표로 표현한 문자열이 주어질 때, 그것이 나타내는 정수 n을 구한다.

난이도: 보통10점 중 6점
유형: 재귀, 구현, 문자열, 정렬
정답자: 아직 제출이 없습니다

문제

Ordinal numbers are an extension of the set of nonnegative integers. For each nonnegative integer $x$ , we will establish the corresponding ordinal number $f (x)$ . The first few ordinal numbers can be defined as follows.

Zero corresponds to an empty set: $f(0) =$ {}.
One corresponds to the set containing the set $f (0)$ as an element: $f(1) =$ { $f(0)$ } $=$ {{}}.
Two corresponds to the set containing the sets $f (0)$ and $f (1)$ as elements: $f(2) =$ { $f(0), f(1)$ } $=$ {{},{{}}}.
And so on: each positive integer $k$ corresponds to the set containing all the previous ordinal numbers as elements. The formula is: $f(k) =$ { $f(0), f(1), \ldots , f(k - 1)$ }.

Next, we can similarly define ordinal numbers that don't correspond to integers. Alas, we won't need them in this problem.

You are given a string describing an ordinal number corresponding to a nonnegative integer $n$ . Find $n$ .

입력

The first line contains the description of an ordinal number corresponding to a certain nonnegative integer $n$ ( $0 \le n \le 15$ ). It consists of the characters "{", ",", and "}".

In the description of each set, each element appears exactly once. However, as a set does not change if we change the order of elements, this order can be arbitrary.

출력

Print the integer $n$ corresponding to the given ordinal number.

예제4

예제 1
입력
```
{}
```
예상 출력
```
0
```
예제 2
입력
```
{{}}
```
예상 출력
```
1
```
예제 3
입력
```
{{},{{}}}
```
예상 출력
```
2
```
예제 4
입력
```
{{{}},{{{}},{}},{}}
```
예상 출력
```
3
```