There are $2N$ cards bearing positive integers. They are arranged in a row from left to right.

Each card bears exactly one positive integer between $1$ and $N$, inclusive. Let $X_i$ be the number on the $i$-th card from the left ($1\le i\le2N$).

For each $k$ with $1\le k\le N$, exactly two cards bear $k$. In other words, each positive integer from $1$ to $N$ appears on exactly two cards.

정올이 calls the number of cards lying between the two cards bearing the positive integer $k$ the "number of cards between $k$".

For example, consider the arrangement in the figure below. Here $N=4$ and $X_1=1,X_2=2,X_3=2,X_4=4,X_5=3,X_6=1,X_7=3,X_8=4$.

• Between the two cards bearing $1$ are cards bearing $2,2,4,3$ in order, so the number of cards between $1$ is $4$.
• There are no cards between the two cards bearing $2$, so the number of cards between $2$ is $0$.
• Only the card bearing $1$ lies between the two cards bearing $3$, so the number of cards between $3$ is $1$.
• Between the two cards bearing $4$ are cards bearing $3,1,3$ in order, so the number of cards between $4$ is $3$.

In this example, the greatest number of cards between any $k$ is the number of cards between $1$, which is $4$.

정올이 wants to find the greatest number of cards between $k$ over all positive integers $k$ from $1$ to $N$.

Given the numbers on the cards in their arranged order, write a program that finds the greatest number of cards between any $k$.

Constraints

• All given numbers are integers.
• $1\le N\le2\,000$
• For each $i$ ($1\le i\le2N$): $1\le X_i\le N$
• For each $k$ ($1\le k\le N$), the number appears exactly twice among $X_1,X_2,\ldots,X_{2N}$.

Subtasks

1. (10 points) $N\le2$
2. (15 points) The answer is $0$ or $1$.
3. (15 points) The answer is $2N-3$ or $2N-2$.
4. (20 points) $N\le500$
5. (40 points) No additional constraints.

Input

The first line contains the integer $N$.

The second line contains $2N$ integers $X_1,X_2,\ldots,X_{2N}$, separated by spaces.

Output

Print the answer on the first line.

Examples

Input 1

4
1 2 2 4 3 1 3 4

Output 1

4

Input 2

4
1 2 3 4 4 3 2 1

Output 2

6