Mr$.$ Jones has $$13,000$ to invest in three types of stocks, low$-$risk, medium$-$risk, and high$-$risk. He invests according to three principles. The amount invested in low$-$risk stocks will be at most $$3,000$ more than the amount invested in medium$-$risk stocks. At least $$5,000$ will be invested in low$-$ and medium$-$risk stocks. No more than $$11,000$ will be invested in medium$-$ and high$-$risk stocks. The expected yields are $6\%$ for low$-$risk stocks, $7\%$ for medium$-$risk stocks, and $8\%$ for high$-$risk stocks. How much money should Mr$.$ Jones invest in each type of stock to maximize his total expected yield?

Mr$.$ Jones should invest $ in low$-$risk stocks, $ in medium$-$risk stocks, and $ in high$-$risk stocks.