The table below gives information about four different crops, their different quality, categories and the regions where they are cultivated. Based on the information given in the table answer the questions below. Crop Quality and Region Distribution
| Type of Crop | Quality | Region |
|---|---|---|
| Crop - 1 | High | R1, R2, R3, R4, R5 |
| Medium | R6, R7, R8 | |
| Low | R9, R10, R11 | |
| Crop - 2 | High | R5, R8, R12 |
| Medium | R9, R13 | |
| Low | R6, R7, R8, R13 | |
| Crop - 3 | High | R2, R6, R7, R13 |
| Medium | R3, R9, R11 | |
| Low | R1, R4 | |
| Crop - 4 | High | R3, R10, R11 |
| Medium | R1, R2, R4 | |
| Low | R5, R9 |
Table : Crop Quality and Region Distribution




| A | B | C | D | Average |
|---|---|---|---|---|
| 3 | 4 | 4 | ? | 4 |
| 3 | ? | 5 | ? | 4 |
| ? | 3 | 3 | ? | 4 |
| ? | ? | ? | ? | 4.25 |
| 4 | 4 | 4 | 4.25 |
For any natural number $k$, let $a_k = 3^k$. The smallest natural number $m$ for which \[ (a_1)^1 \times (a_2)^2 \times \dots \times (a_{20})^{20} \;<\; a_{21} \times a_{22} \times \dots \times a_{20+m} \] is: