Suppose that a pension fund has a series of liabilities to be paid every six months to the pension plan beneficiaries: $$4,500,000,$$$5,100,000,$ $$5,600,000,$$$6,300,000,$$$6,800,000,$$$7,200,000,$$$7,900,000,$ and $$8,600,000.$ The company wishes to construct a portfolio of assets to cover this series of liabilities, such that it is immunized against interest rate risk right now. The company is considering investing in four bonds: $(1)$ a $1-$year Treasury bond with a face value of $$1,000$ and an annual coupon rate of $1\mathrm{.}50\%,(2)$ a $2-$year Treasury bond with a face value of $$1,000$ and an annual coupon rate of $2\mathrm{.}70\%,(3)$ a $3-$year Treasury bond with a face value of $$1,000$ and an annual coupon rate of $2\mathrm{.}90\%,$ and $(4)$ a $4-$year Treasury bond with a face value of $$1,000$ and an annual coupon rate of $3\mathrm{.}20\%.$ All four bonds make $2($semi$-$annual$)$ coupon payments per year. Thus they have $2$ periods, $4$ periods, $6$ periods, and $8$ periods until maturity, respectively. The current yield on all bonds is $3\mathrm{.}17\%.$ How many of each of these four Treasury bonds should the pension fund buy in order to fully fund the liability and be immunized against interest rate risk right now?