CodeForces ~ 996

Allen has a LOT of money. He has $n$

Input

The first and only line of input contains a single integer $n$

Output

Output the minimum number of bills that Allen could receive.

Examples

Input

Output

Input

Output

Input

1000000000

Output

10000000

Note

In the first sample case, Allen can withdraw this with a $100$

In the second sample case, Allen can withdraw two $20$

In the third sample case, Allen can withdraw $100000000$

解题思路：简单贪心

Allen wants to enter a fan zone that occupies a round square and has $n$

There already is a queue of $a_{i}$

Allen uses the following strategy to enter the fan zone:

Initially he stands in the end of the queue in front of the first entrance.
Each minute, if he is not allowed into the fan zone during the minute (meaning he is not the first in the queue), he leaves the current queue and stands in the end of the queue of the next entrance (or the first entrance if he leaves the last entrance).

Determine the entrance through which Allen will finally enter the fan zone.

Input

The first line contains a single integer $n$

The second line contains $n$

Output

Print a single integer — the number of entrance that Allen will use.

Examples

Input

4
2 3 2 0

Output

Input

2
10 10

Output

Input

6
5 2 6 5 7 4

Output

Note

In the first example the number of people (not including Allen) changes as follows: $[2, 3, 2, 0] \to [1, 2, 1, 0] \to [0, 1, 0, 0]$

In the second example the number of people (not including Allen) changes as follows: $[10, 10] \to [9, 9] \to [8, 8] \to [7, 7] \to [6, 6] \to [5, 5] \to [4, 4] \to [3, 3] \to [2, 2] \to [1, 1] \to [0, 0]$

In the third example the number of people (not including Allen) changes as follows: $[5, 2, 6, 5, 7, 4] \to [4, 1, 5, 4, 6, 3] \to [3, 0, 4, 3, 5, 2] \to [2, 0, 3, 2, 4, 1] \to [1, 0, 2, 1, 3, 0] \to [0, 0, 1, 0, 2, 0]$

题意：有n 个元素，而你会按顺序每个等一分钟，看哪个先到0，每过一分钟，都要减1

思路：你可以把每个元素算出一个步数，至少第几步才可以排到这个，首先看这个元素是否>n，大于的话说明还要走几圈，可以算出这个圈数再来算步数

这是我的方法，但是后来看了下大牛的方法，直接算出圈数，选最小的圈数的那个，有相同的圈数的话选最先出现的那个，这样方便了很多

引用大牛博客https://blog.csdn.net/ZscDst/article/details/80807353

#include <bits/stdc++.h>
using namespace std;
const int MAXN = 1e5+5;
const int INF = 0x3f3f3f3f;
int n, ans;
int main()
{
    scanf("%d", &n);
    int MIN = INF;
    for (int i = 1; i <= n; i++)
    {
        int a; scanf("%d", &a);
        if(MIN > (a-i+n)/n)//x*n+i=a =》x=abs(a-i)/n
        {
            MIN = (a-i+n)/n;
            ans = i;
        }
    }
    printf("%d\n", ans);
    return 0;
}

Allen dreams of one day owning a enormous fleet of electric cars, the car of the future! He knows that this will give him a big status boost. As Allen is planning out all of the different types of cars he will own and how he will arrange them, he realizes that he has a problem.

Allen's future parking lot can be represented as a rectangle with $4$

$\text{[math]}$ Illustration to the first example.

However, since Allen would never entrust his cars to anyone else, only one car can be moved at a time. He can drive a car from a space in any of the four cardinal directions to a neighboring empty space. Furthermore, Allen can only move one of his cars into a space on the first or fourth rows if it is the car's designated parking space.

Allen knows he will be a very busy man, and will only have time to move cars at most $20000$

Input

The first line of the input contains two space-separated integers $n$

The next four lines will contain $n$

In the first and last line, an integer $1 \leq x \leq k$

In the second and third line, an integer $1 \leq x \leq k$

Each $x$

Output

If there is a sequence of moves that brings all of the cars to their parking spaces, with at most $20000$

If it is not possible for Allen to move all the cars to the correct spaces with at most $20000$

Examples

Input

Output

Input

Output

-1

Input

Output

2
1 1 1
2 4 1

Note

In the first sample test case, all cars are in front of their spots except car $5$

In the second sample test case, there is only one column, and the cars are in the wrong order, so no cars can move and the task is impossible.

引用大牛博客：https://blog.csdn.net/ZscDst/article/details/80821376

Allen is hosting a formal dinner party. $2 n$

Help Allen find the minimum number of swaps of adjacent positions he must perform to make it so that each couple occupies adjacent positions in the line.

Input

The first line contains a single integer $n$

The second line contains $2 n$

Output

Output a single integer, representing the minimum number of adjacent swaps needed to line the people up so that each pair occupies adjacent positions.

Examples

Input

4
1 1 2 3 3 2 4 4

Output

Input

3
1 1 2 2 3 3

Output

Input

3
3 1 2 3 1 2

Output

Note

In the first sample case, we can transform $11233244 \to 11232344 \to 11223344$

The second sample case already satisfies the constraints; therefore we need $0$

思路：简单贪心，只要遍历一遍，然后再找到当前元素交换过来即可

For a vector $\vec{v} = (x, y)$

Allen had a bit too much to drink at the bar, which is at the origin. There are $n$

Allen doesn't want to wander too far from home (which happens to also be the bar). You need to help him figure out a sequence of moves (a sequence of signs for the vectors) such that his final position $p$

Input

The first line contains a single integer $n$

Each of the following lines contains two space-separated integers $x_{i}$

Output

Output a single line containing $n$

It can be shown that a solution always exists under the given constraints.

Examples

Input

Output

1 1 -1

Input

1
-824590 246031

Output

Input

8
-67761 603277
640586 -396671
46147 -122580
569609 -2112
400 914208
131792 309779
-850150 -486293
5272 721899

Output

1 1 1 1 1 1 1 -1 





思路：贪心+随机算法，（随机算法没听过，今天算是初次见面了）
大牛博客：https://blog.csdn.net/ZscDst/article/details/80818824

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