The north$-$south highway system passing through Albany, New York, can accommodate the capacities shown.

A network diagram between six parties, distributed across five columns, is shown. The left$-$most column contains node $1.$ The second column contains nodes $2,$ and $3.$ The third column contains node $4.$ The fourth column contains node $5.$ The right$-$most column contains node $6.$ Traffic enters Albany from the North at node $1,$ and leaves Albany to the South at node $6.$ Arrows are shown between various locations. The following list contains the numbers placed on the graph.

$1->2$: $2$

$1->3$: $6$

$1->4$: $3$

$21$: $2$

$24$: $1$

$2->5$: $4$

$31$: $6$

$34$: $3$

$3->6$: $2$

$41$: $3$

$42$: $1$

$43$: $3$

$45$: $1$

$4->6$: $3$

$52$: $4$

$54$: $1$

$5->6$: $6$

$63$: $2$

$64$: $3$

$65$: $6$

It is noted that a label $"6"$ by an arrow means a flow capacity of $6,000$ vehicles per hour.

Can the highway system accommodate a north$-$south flow of $10,000$ vehicles per hour?

Yes

No