# The String of 7

Consider a string of $$n$$ $$7$$'s, $$7777\cdots77,$$ into which $$+$$ signs are 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?

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