------
## 最终结论
```python
def maxSizeSlices(slices):
    def calculate(slices):
        n = len(slices) // 3
        dp = [[0] * (n + 1) for _ in range(len(slices) + 1)]

        for i in range(1, len(slices) + 1):
            for j in range(1, min(i, n) + 1):
                dp[i][j] = dp[i - 1][j]  # not taking the current slice
                if i >= 2:  # ensure we can take a slice
                    dp[i][j] = max(dp[i][j], slices[i - 1] + dp[i - 2][j - 1])  # taking the current slice

        return max(dp[i][n] for i in range(len(slices)))

    # Since the pizza is circular, we need to consider two cases:
    # Case 1: We take slices from index 0 to len(slices)-2 (excluding last slice)
    # Case 2: We take slices from index 1 to len(slices)-1 (excluding first slice)
    return max(calculate(slices[:-1]), calculate(slices[1:]))

# Example usage:
slices1 = [1,2,3,4,5,6]
print(maxSizeSlices(slices1))  # Output: 10

slices2 = [8,9,8,6,1,1]
print(maxSizeSlices(slices2))  # Output: 16

slices3 = [4,1,2,5,8,3,1,9,7]
print(maxSizeSlices(slices3))  # Output: 21

slices4 = [3,1,2]
print(maxSizeSlices(slices4))  # Output: 3
```

This solution takes into account the circular nature of the pizza by considering two possible scenarios for selecting slices. It uses dynamic programming to compute the maximum sum of selected slices while respecting the selection rules.