Starting with a sequence of $n 1's$, you can insert plus signs to get various sums. For example, when $n = 10$,  you can get the sum $1 + 1 + 1 + 11 + 11 + 111 = 136$, and the sum $1 + 1 + 11 + 111 + 111 = 235$.  Find the number of values of $n$ so that the sum of $1111$ is possible.

Let's think step by step and output the final answer within \boxed{}.
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