Suppose you purchase a portfolio with two coupon bonds A$,$ B at t $=0.$ Both bonds are of maturity in $2$ years $($T $=2).$ Bond A has semi$-$annual coupons while bond B month coupons. $($i$)$ Please determine there are how many Zig$-$Zag points $($i$.$e$.,$ discontinuous points$)$ for duration function $$d$($s$),$ s in $[0,2]$ on your portfolio.$($ii$)$ In case you add a new zero$-$coupon bond C in your portfolio with maturity in $1$ year, how many Zig$-$Zag points in this case?