A group of n friends wrote a math contest consisting of eight short-answer problems S_{1}, S_{2}, S_{3}, S_{4}, S_{5}, S_{6}, S_{7}, S_{8}, and four full-solution problems F_{1}, F_{2}, F_{3}, F_{4}. Each person in the group correctly solved exactly 11 of the 12 problems. We create an 8 \times 4 table. Inside the square located in the i^{\text {th }} row and j^{\text {th }} column, we write down the number of people who correctly solved both problem S_{i} and problem F_{j}. If the 32 entries in the table sum to 256, what is the value of n?
