A flow network is a directed graph which has a source and a sink. 

In a flow network, each edge (u,v) has a capacity c(u,v). Each edge receives a flow, but the amount of flow on the edge can not exceed the corresponding capacity. 

Find the maximum flow from the source to the sink.

The first line consists of $|V|, |E|$ is the number of vertices and edges of the flow network respectively. The vertices in $G$ are named with the numbers 0, 1,..., |V|−1|. The source is 0 and the sink is |V|−1|.

In the following |E| lines, $u_i, v_i, c_i$ represent $i$-th edge of the flow network. A pair of $u_i$ and $v_i$ denotes that there is an edge from $u_i$ to $v_i$ and $c_i$ is the capacity of $i$-th edge.