Given $N$ integers in the range $[-50\, 000, 50\, 000]$, how many ways are there to pick three integers $a_ i$, $a_ j$, $a_ k$, such that $i$, $j$, $k$ are pairwise distinct and $a_ i + a_ j = a_ k$? Two ways are different if their ordered triples $(i, j, k)$ of indices are different.

The first line of input consists of a single integer $N$ ($1 \leq N \leq 200\, 000$). The next line consists of $N$ space-separated integers $a_1, a_2, \dots , a_ N$.

Output an integer representing the number of ways.

Sample Input 1 | Sample Output 1 |
---|---|

4 1 2 3 4 |
4 |

Sample Input 2 | Sample Output 2 |
---|---|

6 1 1 3 3 4 6 |
10 |