Paint the Roads

A city has $N$ buildings and $M$ roads. Road $i$ connects building $u_i$ and building $v_i$ in both directions. No two roads connect the same pair of buildings. Each road is painted with one of $K$ colors, and road $i$ has color $c_i$. The paint is still wet, so the building visited right after traveling along road $i$ is painted over with color $c_i$. Initially, every building has color $0$. ($1 \le i \le M$)

Performance artist Eunha wants to paint the buildings using the following method.

• Eunha picks a starting building and goes there.
• Repeat the following step until every building has its desired color.
  • From her current building $a$, she moves along a road with color $p$ to an adjacent building $b$. She may visit the same building many times. There must exist an $i$ with $(a,b,p) = (u_i,v_i,c_i)$ or $(v_i,u_i,c_i)$.
  • She paints building $b$ with color $p$, regardless of its previous color.

Eunha wants building $j$ to have color $r_j$ for every $j$ with $1 \le j \le N$. Determine whether this is possible. If it is, output one way to do it.

The first line contains the number of buildings $N$, the number of roads $M$, and the number of colors $K$, separated by spaces. ($2 \le N \le 100\,000$, $1 \le M \le 200\,000$, $1 \le K \le 100\,000$)

The second line contains the target colors $r_1, r_2, \cdots, r_N$, separated by spaces. ($1 \le r_j \le K$)

Each of the next $M$ lines contains $u_i$, $v_i$, and $c_i$, separated by spaces. ($1 \le u_i < v_i \le N$, $1 \le c_i \le K$, and if $i \ne j$ then $(u_i, v_i) \ne (u_j, v_j)$)

All input values are integers.

For every $j$ with $1 \le j \le N$, if building $j$ can be painted with color $r_j$, print YES on the first line. Otherwise print NO.

If you print YES, print the number of buildings Eunha visits on the second line, and the building numbers she visits in order on the third line, separated by spaces. The total number of visits must not exceed $1\,000\,000$. After visiting the buildings in this order, every building $j$ must have color $r_j$. It can be proven that whenever painting is possible, it can be done with at most $1\,000\,000$ visits for every valid input.