Sum of Some Squared Divisors

Let \(1 = d_1 < d_2 < \ldots < d_k =N \) be all the divisors of \(N\) arranged in increasing order. Given that \(N = d_1 ^2 + d_2 ^2 + d_3 ^2 + d_4 ^2 \), determine \(N\).

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