A tea shop offers tea in cups of three different sizes. The product of the prices, in $\text{INR},$ of three different sizes is equal to $800.$ The prices of the smallest size and the medium size are in the ratio $2:5.$ If the shop owner decides to increase the prices of the smallest and the medium ones by $\text{INR} \; 6$ keeping the price of the largest size unchanged, the product then changes to $3200.$ The sum of the original prices of three different sizes, in $\text{INR},$ is