Problem Statement

Given is a weighted undirected connected graph G with N vertices and M edges, which may contain self-loops and multi-edges.
The vertices are labeled as Vertex $1, Vertex 2, \dots, Vertex N$.
The edges are labeled as Edge $1, Edge 2, \ldots, Edge M. Edge i connects Vertex a_i$ and Vertex b_i and has a weight of c_i. Here, for every pair of integers (i, j) such that $1 \leq i \lt j \leq M, c_i \neq c_j$ holds.
Process the Q queries explained below.
The i-th query gives a triple of integers (u_i, v_i, w_i). Here, for every integer j such that $1 \leq j \leq M, w_i \neq c_j$ holds.
Let e_i be an undirected edge that connects Vertex u_i and Vertex v_i and has a weight of w_i. Consider the graph G_i obtained by adding e_i to G.
It can be proved that the minimum spanning tree T_i of G_i is uniquely determined. Does T_i contain e_i? Print the answer as Yes or No.
Note that the queries do not change T. In other words, even though Query i considers the graph obtained by adding e_i to G, the G in other queries does not have e_i.

What is minimum spanning tree?
The spanning tree of G is a tree with all of the vertices in G and some of the edges in G.
The minimum spanning tree of G is the tree with the minimum total weight of edges among the spanning trees of G.

Input

Input is given from Standard Input in the following format:
N M Q
a_1 b_1 c_1
a_2 b_2 c_2
$\vdots$
a_M b_M c_M
u_1 v_1 w_1
u_2 v_2 w_2
$\vdots$
u_Q v_Q w_Q

Output

Print Q lines. The i-th line should contain the answer to Query i: Yes or No.

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $N - 1 \leq M \leq 2 \times 10^5$
• $1 \leq a_i \leq N (1 \leq i \leq M)$
• $1 \leq b_i \leq N (1 \leq i \leq M)$
• $1 \leq c_i \leq 10^9 (1 \leq i \leq M)$
• $c_i \neq c_j (1 \leq i \lt j \leq M)$
• The graph G is connected.
• $1 \leq Q \leq 2 \times 10^5$
• $1 \leq u_i \leq N (1 \leq i \leq Q)$
• $1 \leq v_i \leq N (1 \leq i \leq Q)$
• $1 \leq w_i \leq 10^9 (1 \leq i \leq Q)$
• $w_i \neq c_j (1 \leq i \leq Q, 1 \leq j \leq M)$
• All values in input are integers.

Sample Input 1

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

Sample Output 1

Yes
No
Yes

Below, let (u,v,w) denote an undirected edge that connects Vertex u and Vertex v and has the weight of w.
Here is an illustration of G:

For example, Query 1 considers the graph G_1 obtained by adding e_1 = (1,3,1) to G. The minimum spanning tree T_1 of G_1 has the edge set $\lbrace (1,2,2),(1,3,1),(2,4,5),(3,5,8) \rbrace, which contains e_1$, so Yes should be printed.

Sample Input 2

2 3 2
1 2 100
1 2 1000000000
1 1 1
1 2 2
1 1 5

Sample Output 2

Yes
No

见题面 Input 部分

见题面 Output 部分