More sums of squares

54841=317×173.\large 54841 = 317 \times 173. 54841, whose prime factor decomposition is given above, can be written as the sum of two perfect squares in two different ways:

54841=a2+b2=c2+d2,54841 = a^2 + b^2 = c^2 + d^2,

where a,b,ca,b,c and dd are distinct positive integers. Find the sum a+b+c+da+b+c+d.

Hint: 317=196+121317 = 196 + 121, and 173=169+4173 = 169 + 4.

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