Pesley has randomly generated two hidden permutations and of length (or at least as random as a computer can). The permutation contains distinct values from to . He wants you to find any indices and such that . Of course, he won't make it that easy and will only give you guesses to do so. After making a guess, he will respond with the values of and . Can you find any such pair of indices?

#### Constraints

**For this problem, you will NOT be required to pass ANY of the samples in order to receive points.**

For all subtasks:

and are selected uniformly at random (subject to the limitations of a computer).

##### Subtask 1 [15%]

##### Subtask 2 [17%]

##### Subtask 3 [68%]

No additional constraints.

#### Interaction

The first line contains the integer , the length of the permutations.

You will then begin making guesses. For each guess, output two space-separated integers , on a single line **terminated by a \n character**. and must be satisfied. Pesley will then respond with two space-separated integers , (followed by a

`\n`

character), representing the values in the first and second permutations at indices and . If , then you have found the indices and will receive an **Accepted**verdict. Otherwise, you can continue to make more guesses until you run out, in which case, you will receive a

**Wrong Answer**verdict.

**If at any point you attempt an invalid operation (such as an invalid output format, failure to provide any output, or index out of bounds), -1 will be outputted (followed by a \n character). When this happens, you should terminate your program to avoid reading from a closed input stream, and you will receive a verdict of Wrong Answer (Presentation Error). Otherwise, the verdict may be undefined.**

**Please note that you may need to flush stdout after each operation. In C++, this can be done with fflush(stdout) or cout << flush (depending on whether you use printf or cout). In Java, this can be done with System.out.flush(). In Python, you can use sys.stdout.flush().**

#### Sample Interaction

`>>>`

denotes your output. Do not print this out.

```
4
>>> 1 2
3 4
>>> 4 3
4 2
>>> 3 1
1 1
```

#### Sample Explanation

In this example, and . is one possible pair of indices as .

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