Which of the following are true about the Bellman$-$Ford single source shortest path algorithm? Select all that apply.

$1.$ If the input graph has n vertices and m edges, the algorithm will always terminate in time O$($nm$).$

$2.$ The algorithm is only guaranteed to be correct when the edge weights are non$-$negative

$3.$ The algorithm can detect if a graph has a negative weight cycle.

$4.$ If in a round of Bellman$-$Ford all edges are relaxed and no distance value is updated, then no distance value will be updated for the rest of the algorithm.