Get Max Discount Pairs

Count product pairs with distinct indices i<j such that price[i]+price[j] equals 3^e for some non-negative integer e, including 3^0=1. Different products with the same price are counted as different index combinations.

输入格式

The first line contains n; the second line contains the prices. This site uses 1≤n≤200000, 0≤price≤10^9.

输出格式

Output a single integer, the answer.

样例 1

输入：

3
2 1 8

输出：

2

样例 2

输入：

3
0 1 1

输出：

2

样例 3

输入：

4
1 1 2 2

输出：

4

样例说明

The answers are 2, 2 and 4.