More sums of squares

Number Theory Level 5

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

$54841 = a^2 + b^2 = c^2 + d^2,$

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

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