For real numbers a and b, define the sequence \{x_{a, b}(n)\} as follows: x_{a, b}(1)=a, x_{a, b}(2)=b, and for n>1, x_{a, b}(n+1)=\left(x_{a, b}(n-1)\right)^2+\left(x_{a, b}(n)\right)^2. For real numbers c and d, define the sequence \{y_{c, d}(n)\} as follows: y_{c, d}(1)=c, y_{c, d}(2)=d, and for n>1, y_{c, d}(n+1)= \left(y_{c, d}(n-1)+y_{c, d}(n)\right)^2. Call (a, b, c) a good triple if there exists d such that for all n sufficiently large, y_{c, d}(n)=\left(x_{a, b}(n)\right)^2. For some (a, b) there are exactly three values of c that make (a, b, c) a good triple. Among these pairs (a, b), compute the maximum value of \lfloor 100(a+b)\rfloor.