Let x1,x2,… be a sequence of 0,1, such that it satisfies the following three conditions:
1) x2=x100=1, xi=0 for 1≤i≤100 and i=2,100;
2) x2n−1=xn−50+1,x2n=xn−50 for 51≤n≤100;
3) x2n=xn−50,x2n−1=xn−50+xn−100 for n>100.
Show that the sequence is periodic.