1004C. Sonya and Robots

Since Sonya is interested in robotics too, she decided to construct robots that will read and recognize numbers.

Sonya has drawn $n$

numbers in a row, $a_i$ is located in the $i$

-th position. She also has put a robot at each end of the row (to the left of the first number and to the right of the last number). Sonya will give a number to each robot (they can be either same or different) and run them. When a robot is running, it is moving toward to another robot, reading numbers in the row. When a robot is reading a number that is equal to the number that was given to that robot, it will turn off and stay in the same position.

Sonya does not want robots to break, so she will give such numbers that robots will stop before they meet. That is, the girl wants them to stop at different positions so that the first robot is to the left of the second one.

For example, if the numbers $[1,5,4,1,3]$

are written, and Sonya gives the number $1$ to the first robot and the number $4$ to the second one, the first robot will stop in the $1$-st position while the second one in the $3$-rd position. In that case, robots will not meet each other. As a result, robots will not be broken. But if Sonya gives the number $4$ to the first robot and the number $5$ to the second one, they will meet since the first robot will stop in the $3$-rd position while the second one is in the $2$

-nd position.

Sonya understands that it does not make sense to give a number that is not written in the row because a robot will not find this number and will meet the other robot.

Sonya is now interested in finding the number of different pairs that she can give to robots so that they will not meet. In other words, she wants to know the number of pairs ($p$

, $q$), where she will give $p$ to the first robot and $q$ to the second one. Pairs ( $p_i$, $q_i$) and ( $p_j$, $q_j$) are different if $p_i\ne p_j$ or $q_i\ne q_j$

.

Unfortunately, Sonya is busy fixing robots that broke after a failed launch. That is why she is asking you to find the number of pairs that she can give to robots so that they will not meet.

Input

The first line contains a single integer $n$

( $1\le n\le {10}^5$

) — the number of numbers in a row.

The second line contains $n$

integers $a_1,a_2,\dots ,a_n$ ( $1\le a_i\le {10}^5$

) — the numbers in a row.

Output

Print one number — the number of possible pairs that Sonya can give to robots so that they will not meet.

Examples

Input

Copy

5
1 5 4 1 3

Output

Copy

9

Input

Copy

7
1 2 1 1 1 3 2

Output

Copy

7

Note

In the first example, Sonya can give pairs ($1$

, $1$), ( $1$, $3$), ( $1$, $4$), ( $1$, $5$), ( $4$, $1$), ( $4$, $3$), ( $5$, $1$), ( $5$, $3$), and ( $5$, $4$

).

In the second example, Sonya can give pairs ($1$

, $1$), ($1$, $2$), ($1$, $3$), ($2$, $1$), ($2$, $2$), ($2$, $3$), and ($3$, $2$).

题意：给你n个数，从每个数起向后找一个数，使得这两数组成一个数对，求一共有多少个不同的数对

思路：记录每种数字左边一共有多少个不同种类的数字，则这些数字与当前数字可以构成一个数字对。

代码：

#include
#include
#include
using namespace std;
typedef long long LL;
const int N = 100005;
int arr[N],vis[N];
setst;
int main(){ 
	int n;
	scanf("%d",&n);
	for(int i=0;i