Show that a sequence d1, d2, . . . , dn of nonnegative integers in non increasing

Question:

Show that a sequence d1, d2, . . . , dn of nonnegative integers in non increasing order is a graphic sequence if and only if the sequence obtained by reordering the terms of the sequence d2 − 1, . . . , dd1+1 − 1, dd1+2, . . . , dn so that the terms are in non increasing order is a graphic sequence.