Work stealing is a scheduling strategy for multithreaded computer programs. It solves the problem of executing a dynamically multithreaded computation. In a work stealing scheduler, each processor has a queue of work items to perform. Each work item consists of a series of instructions to be executed sequentially and those instructions are prerequisite of each other.

Let’s say you want to implement your own scheduler. You are given \(n\) prerequisite pairs \(i, j\) which means that you must execute instruction \(j\) before instruction \(i\). You are asked to find a way to execute every instruction in the prerequisite list.

Input

The first line contains one integer, \(n\) — the number of prerequisites.

Each of the next \(n\) lines contain two integers \(i\) and \(j\), meaning that instruction \(j\) must be executed before instruction \(i\).

• \(1 \le i, j \le 1000\)
• \(i \ne j\)

All the pairs \(i, j\) are distinct.

There is no cyclic dependency between instructions.

Output

First, print the number of instructions to execute, \(m\).

Afterwards, print \(m\) integers representing the indices of the instructions to execute from first to last.

Example

Input 1:

1
2 7

Output 1:

2
7 2

Input 2:

4
2 1
3 1
4 2
4 3

Output 2:

4
1 2 3 4

Explanation

Input 1: There are 2 instructions to execute, and to execute instruction 2 scheduler should execute instruction 7. So the correct course order is 7 2.

Input 2: There are 4 instructions to execute, and to execute instruction 4, scheduler should execute instruction 2 and instruction 3. Both instruction 2 and instruction 3 should also be executed after instruction 1. So, one correct order is 1 2 3 4. 1 3 2 4 is also acceptable.