**TRUE**?

$$\,\,\,\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,\,\,\,\,\,$$ If $$e$$ is the lightest edge of __some__ cycle in $$G,$$ then every $$MST$$ of $$G$$

$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$__includes__ $$e$$

$$\,\,\,\,\,\,\,\,{\rm I}{\rm I}.\,\,\,\,\,\,\,\,\,\,$$ If $$e$$ is the heaviest edge of __some__ cycle in $$G,$$ then every $$MST$$ of $$G$$

$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$__excludes__ $$e$$

The largest possible integer value of $$x,$$ for which at least one shortest path between some pair of vertices will contain the edge with weight $$x$$ is _________________.

1 | 2 | 5 | 14 |
---|---|---|---|

3 | 4 | 6 | 23 |

10 | 12 | 18 | 25 |

31 | ∞ |
∞ | ∞ |

When an element is removed from a Young tableau, other elements should be moved into its place so that the resulting table is still a Young tableau (unfilled entries may be filled in with a $$\infty $$). The minimum number of entries (other than $$1$$) to be shifted, to remove $$1$$ from the given Young tableau is ______________.