2004 AIME II Problem 14

Consider a string of n 7’s, \begin{array}{llllllll}7 & 7 & 7 & 7 & \ldots & 7 & 7, & \text { into which }+ \text { signs are }\end{array} inserted to produce an arithmetic expression. For example, 7+77+777+7+7= 875 could be obtained from eight 7's in this way. For how many values of n is it possible to insert + signs so that the resulting expression has value 7000 ?