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Zhenya studies electricity at Physics practice lessons in his school. His next task is to analyze an electrical network.
Electrical network is the set of nodes, connected by wires. One of the nodes is a source node, and another one is a sink node. The electrical network in this task is correct.
Electrical network is called correct iff it can be constructed using following rules:
The picture shows examples of correct networks.
|Basic network||Network from example 1||Network from example 2||Network from example 3|
|Other examples of correct networks|
Zhenya doesn't like Physics, but he likes Graph Theory. So, instead of doing his task, he wants to count the number of ways to remove some wires from the network, so that the remaining wires formed a tree: there was exactly one path by wires from any node to any other node.
That number could be very big, so Zhenya wants to find its reminder modulo $998\,244\,353$.
The first line of input contains two itnegers $n$ and $m$ --- number of nodes in the network and the number of wires ($1 \le n,m \le 100\,000$).
The following $m$ lines contain the description of wires. Each of them contains two integers $a$ and $b$, they mean that nodes $a$ and $b$ are connected by a wire ($1 \le a, b \le n$; $a \ne b$).
It's guaranteed, that the given network is correct. The source node is the node number $1$, and the sink node is the node number $n$. Note, that correct networks can have several wires between a pair of nodes.
Print one integer --- the number of ways to remove the wires, modulo $998\,244\,353$.
3 3 1 2 2 3 3 1
6 7 1 2 1 3 1 6 2 4 3 5 4 6 5 6
2 2 1 2 1 2
In the first and in the third exmaple any single wire can be removed.
In the second example either wire $(1, 6)$ and any other wire can be removed, or one wire from each of the chains $1-2-4-6$ and $1-3-5-6$.