The 4-digit integer \(\overline{wxyz} \) can be written as \(a^3 w + b^2x + cy + dz\).

If \( abc + bcd + abd + acd + abcd + 2a + 3b + 4c + 5d + a^2 + b^2 + c^2 + d^2\) is equal to another 4-digit integer \( \overline{klmn}\), what is the value of \( k^2 + l^2 + m^2 + n^2 + 2k + 2l + 2m + 2n + klmn\)?

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