Drop the Bit

Interview

Time limit1sMemory limit1024 MB

Summary

Given N and the counts of 1 bits in two N-bit binary numbers x and y, find the maximum possible value of x XOR y.

Level: Easy3 of 10
Topics: Math, Greedy
Solved: No attempts yet

Problem

Wrapper H.Arc, who plays with bits, came up with two $N$ -digit binary numbers $x$ and $y$ one day when composing was not going well. He then left a note:

In $x$ , $a$ digits are $1$ , and in $y$ , $b$ digits are $1$ . Both numbers may start with $0$ .

You found this note and wondered about the maximum value of $x \oplus y$ over all pairs $x$ , $y$ that H.Arc could have come up with. Find this value.

Input

The first line contains $N$ . $(1 \le N \le 10)$

The second line contains $a$ and $b$ , separated by a space. $(0 \le a, b \le N)$

Output

Print the maximum value of $x \oplus y$ .

Hint

$\oplus$ is the bitwise XOR operation. For two binary numbers $a, b$ , the $i$ -th digit of $a \oplus b$ is $0$ if the $i$ -th digits of $a$ and $b$ are equal, and $1$ otherwise.

Examples2

Example 1
Input
```
2
1 1
```
Expected output
```
3
```
Example 2
Input
```
3
2 2
```
Expected output
```
6
```