**Time limit:**1.00 s**Memory limit:**512 MB

However, there is a problem: Kaaleppi has recently robbed a bank in city $c$ and can't enter the city, because the local police would catch him. Your task is to find out if there is a route from city $a$ to city $b$ that does not visit city $c$.

As an additional challenge, you have to process $q$ queries where $a$, $b$ and $c$ vary.

**Input**

The first input line has three integers $n$, $m$ and $q$: the number of cities, roads and queries. The cities are numbered $1,2,\dots,n$.

Then, there are $m$ lines describing the roads. Each line has two integers $a$ and $b$: there is a road between cities $a$ and $b$. Each road is bidirectional.

Finally, there are $q$ lines describing the queries. Each line has three integers $a$, $b$ and $c$: is there a route from city $a$ to city $b$ that does not visit city $c$?

You can assume that there is a route between any two cities.

**Output**

For each query, print "YES", if there is such a route, and "NO" otherwise.

**Constraints**

- $1 \le n \le 10^5$

- $1 \le m \le 2 \cdot 10^5$

- $1 \le q \le 10^5$

- $1 \le a,b,c \le n$

**Example**

Input:

`5 6 3`

1 2

1 3

2 3

2 4

3 4

4 5

1 4 2

3 5 4

3 5 2

Output:

`YES`

NO

YES