------
## 最终结论
```python
from collections import Counter
from math import comb

def count_tuples(A, target):
    MOD = 10**9 + 7
    count = 0
    n = len(A)
    
    # Initialize counter and sort the array
    count_map = Counter(A)
    unique_values = sorted(count_map.keys())
    
    for i in range(len(unique_values)):
        for j in range(i, len(unique_values)):
            k_value = target - unique_values[i] - unique_values[j]
            if k_value < unique_values[j]:
                continue
            
            if k_value in count_map:
                if unique_values[i] == unique_values[j] == k_value:
                    # All three numbers are the same
                    count += comb(count_map[unique_values[i]], 3)
                elif unique_values[i] == unique_values[j]:
                    # Two numbers are the same (i and j)
                    count += comb(count_map[unique_values[i]], 2) * count_map[k_value]
                elif unique_values[j] == k_value:
                    # Two numbers are the same (j and k)
                    count += count_map[unique_values[i]] * comb(count_map[unique_values[j]], 2)
                else:
                    # All three numbers are different
                    count += count_map[unique_values[i]] * count_map[unique_values[j]] * count_map[k_value]
                
                count %= MOD
    
    return count

# Example usage:
A1 = [1,1,2,2,3,3,4,4,5,5]
target1 = 8
print(count_tuples(A1, target1))  # Output: 20

A2 = [1,1,2,2,2,2]
target2 = 5
print(count_tuples(A2, target2))  # Output: 12
```