### ** routes**

## Problem Description

Rar lives in a town with *N* blocks and *E* roads connecting two blocks *A*_{i} and *B*_{i}.

To be healthy, Rar has created an exercise regime for himself, lasting *D* days. Each day, Rar will travel a route from block *X*_{i} to block *Y*_{i}. A valid route is defined as a sequence of blocks, starting with *X*_{i} and ending with *Y*_{i}, such that Rar will travel from one block to the next in order.

Rar is weird. On some days, he feels like picking a route with an *odd* number of roads, and on other days he feels like picking one with an *even* number of roads.

For each day, help Rar determine whether there exists an odd and/or even length path from his designated start and end blocks.

## Input

The first line of input will contain three integers, *N*, *E* and *D*.

The next *E* lines of input will contain two integers each, *A*_{i} and *B*_{i}.

The next *D* lines of input will contain two integers each, *X*_{i} and *Y*_{i}.

## Output

For each day, the output should contain a string ("odd", "even", "none" or "both"), describing the parity of the available paths.

## Limits

0 ≤ A_{i}, B_{i}, X_{i}, Y_{i} < N.

Subtask 1 (15%): 1 ≤ N, E ≤ 1000. 1 ≤ Q ≤ 10^{6}.

Subtask 2 (16%): 1 ≤ N, E ≤ 500000. Q = 1.

Subtask 3 (20%): 1 ≤ N ≤ 500000. 1 ≤ Q ≤ 10^{6}. E = N - 1. The graph is a **tree**.

Subtask 4 (23%): 1 ≤ N ≤ 500000. 1 ≤ Q ≤ 10^{6}. E = N. The graph is connected.

Subtask 5 (26%): 1 ≤ N, E ≤ 500000. 1 ≤ Q ≤ 10^{6}.

Subtask 6 (0%): Sample Testcases.

## Sample Testcase 1

### Input

6 5 3
0 1
1 5
1 2
2 4
2 3
3 5
2 1
1 4

### Output

odd
odd
even

## Sample Testcase 2

### Input

9 8 5
0 1
1 2
4 7
4 5
5 6
5 8
6 7
0 2
3 7
1 2
5 7
4 5
3 0

### Output

none
both
even
odd
none