Mr. Malnar enjoys walking, and therefore he is interested in a walk through the fragrant city gardens. We can imagine the city gardens as a graph where the gardens are labeled with numbers from $1$ to $n$. There are exactly $m$ undirected unique edges between them. We also know that the garden labeled with the number $i$ has an aromaticity coefficient $A_i$.

It is well known to everyone that for a walk to be adventurous, the aromaticity must have its ups and downs, i.e., if we denote the gardens visited in the walk as $v_1, v_2, \dots, v_k$ (which are not necessarily distinct), it must hold that $A_{v_1} < A_{v_2} > A_{v_3} < A_{v_4} \dots$

Now, Mr. Malnar is interested in which gardens he can reach by an adventurous walk starting from garden $1$ (it is possible that Mr. Malnar's walk ends immediately in that garden).

Input

The first line contains the natural numbers $n$ ($1 \le n \le 3 \cdot 10^5$) and $m$ ($1 \le m \le 3 \cdot 10^5$) from the problem description.

The next line contains $n$ numbers, where the $i$-th number is $A_i$ ($1 \le A_i \le 10^9$).

In each of the next $m$ lines, there are two numbers $u_i$ and $v_i$ ($1 \le u_i, v_i \le n, v_i \neq u_i$) which indicate that gardens $u_i$ and $v_i$ are connected by an edge.

Output

In the first line, you need to print the number $k$, the number of gardens Mr. Malnar can reach.

In the next line, you need to print $k$ numbers in ascending order, the labels of the gardens Mr. Malnar can reach.

Examples

Input 1

5 7
3 5 3 1 3
2 1
4 1
3 1
2 3
5 3
4 3
4 5

Output 1

3
1 2 3

Input 2

6 6
4 6 3 6 6 10
4 6
3 1
4 2
2 1
5 1
4 3

Output 2

3
1 2 5