Problem Description

Snuke has a directed graph with $N$ vertices numbered from $1$ to $N$. Initially, this graph has no edges. Snuke's task is to add $M$ edges to this graph so that for any pair of vertices $(u, v)$, it is possible to reach $v$ from $u$ by following the edges.

Edges are added using two sequences $a$ and $b$ of length $M$. Snuke can freely rearrange the elements of $a$ and $b$ (but cannot swap elements between $a$ and $b$), and then use these sequences to add $M$ directed edges to the graph.

For the $i$-th edge, Snuke can add either of the following edges:

• A directed edge from vertex $a_i$ to $b_i$
• A directed edge from vertex $b_i$ to $a_i$

Is it possible for Snuke to complete his task? If possible, show an example of how to add the edges.

Input Format

The input is given from the standard input in the following format:

$N$ $M$ $a_1$ $a_2$ $...$ $a_{M}$ $b_1$ $b_2$ $...$ $b_{M}$

Output Format

If Snuke's task is achievable, output Yes. Otherwise, output No. If achievable, output $M$ lines in the following format to show how to add the edges:

$x_1$ $c_1$ $y_1$ $ : $ $x_{M}$ $c_{M}$ $y_{M}$

Here, $c_i$ being > indicates a directed edge from $x_i$ to $y_i$, and $c_i$ being < indicates a directed edge from $y_i$ to $x_i$. $x$ and $y$ are the rearranged sequences of $a$ and $b$, respectively, and the solution is correct if for any pair of vertices $u, v$, it is possible to reach $v$ from $u$ by following the edges.

Sample Input and Output

Sample Input #1

3 6
1 2 3 1 1 1
3 2 1 1 1 2

Sample Output #1

Yes
1 > 2
1 < 2
1 > 3
3 > 1
1 < 1
2 > 1

Sample Input #2

3 1
1
2

Sample Output #2

No

Sample Input #3

13 29
2 8 4 5 5 8 2 9 2 5 9 4 3 8 4 2 12 4 4 12 8 8 3 12 3 9 4 8 9
6 1 1 11 12 6 9 12 6 13 10 11 13 6 10 10 11 3 10 13 10 13 7 7 11 7 11 10 12

Sample Output #3

Yes
2 > 6
12 < 1
5 > 1
4 > 11
2 < 12
12 < 6
4 < 9
3 > 12
8 < 6
9 > 13
4 < 10
3 < 11
4 < 13
2 < 6
8 > 10
5 > 10
4 < 11
12 < 3
8 < 10
9 < 13
4 > 10
9 < 13
8 > 7
8 < 7
5 < 11
2 < 7
9 < 11
8 < 10
3 > 12

Notes/Hints

Constraints

• $1 \leq N, M \leq 2 \times 10^5$
• $1 \leq a_i, b_i \leq N$
• All given inputs are integers

Sample Explanation 1

• By constructing a graph as shown in the figure below, Snuke can achieve his task. Note that the final graph may include multiple edges or self-loops.

Sample Explanation 2

• No matter how edges are added, Snuke cannot achieve his task.

见题面 Input 部分

见题面 Output 部分