Problem:
Score : 500 points

Problem Statement

There are N children standing in a line from left to right. The activeness of the i-th child from the left is A_i.

You can rearrange these children just one time in any order you like.

When a child who originally occupies the x-th position from the left in the line moves to the y-th position from the left, that child earns A_x \times |x-y| happiness points.

Find the maximum total happiness points the children can earn.

Constraints

2 \leq N \leq 2000

1 \leq A_i \leq 10^9

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the maximum total happiness points the children can earn.

Sample Input 1

4
1 3 4 2

Sample Output 1

20

If we move the 1-st child from the left to the 3-rd position from the left, the 2-nd child to the 4-th position, the 3-rd child to the 1-st position, and the 4-th child to the 2-nd position, the children earns 1 \times |1-3|+3 \times |2-4|+4 \times |3-1|+2 \times |4-2|=20 happiness points in total.

Sample Input 2

6
5 5 6 1 1 1

Sample Output 2

58

Sample Input 3

6
8 6 9 1 2 1

Sample Output 3

85

Solution in C (GCC 9.2.1) (judge verdict: Runtime Error)

#include <stdio.h>
#include <stdlib.h>

#define max(a, b) ((a)>(b)?(a):(b))

struct node {
	struct node *left;
	struct node *right;
	int index;
	int activity;
};

struct node *
insert(struct node *p, int act, int index)
{
	int cmp;
	if (p == NULL) {
		p = (struct node *)malloc(sizeof(struct node));
		p->left = (struct node *)NULL;
		p->right = (struct node *)NULL;
		p->index = index;
		p->activity = act;
		return p;
	} else {
		if ( act < p->activity) {
			p->left = insert(p->left, act, index);
			return p;
		} else if (act >= p->activity) {
			p->right = insert(p->right, act, index);
			return p;
		} else {
			printf("This case is not exist");
		}
	}
}

int depthNode(struct node *p, int n, int *idx) {
	if (p->right == NULL) {
		idx[n] = p->index;
		n++;
	} else {
		n = depthNode(p->right, n, idx);
		idx[n] = p->index;
		n++;
	}
	
	if (p->left == NULL) {
		return n;
	} else {
		n = depthNode(p->left, n, idx);
	}
	return n;
}

int main()
{
	int i, j, N;
	int ix, iy;
	int ixend, iyend;
	int step;
	long *A;
	long **DP;
	int *Index;
	int *isVacantFrom;
	int *LorR;
	long maxValueX, maxValueY, temp;
	int maxIndexX, maxIndexY;
	int n;
	int ret;
	int act;
	int nextcase;
	unsigned long icase, tempbit;
	unsigned long nall;
	int gonext;
	
	struct node *root = (struct node *)NULL;
	
	ret = scanf("%d", &N);
	A = (long *) malloc(sizeof(long)*N);
	DP = (long **) malloc(sizeof(long *)*N);
	
	for (ix = 0; ix < N; ix++) {
		DP[ix] = (long *) malloc(sizeof(long)*N);
		for (iy = 0; iy < N; iy++)
			DP[ix][iy] = 0;
	}
	
	Index = (int *) malloc(sizeof(int)*N);
	
	for (i = 0; i < N; i++) {
		ret = scanf(" %ld", &A[i]);
		root = insert(root, A[i], i);
	}

	n = depthNode(root, 0, Index);
	
	for (i = 0; i < n; i++) {
		//fprintf(stderr, "%d %d %ld\n", i, Index[i], A[Index[i]]);
	}
	
	//fprintf(stderr, "N: %d\n", N);
	//for (i = 0; i < N; i++)
			//fprintf(stderr, "A[%d]:%ld ", i, A[i]);
	//fprintf(stderr, "\n");
	isVacantFrom = (int *)malloc(sizeof(int)*N);
	LorR = (int *)malloc(sizeof(int)*N);
	
	nall = 1;
	for (i = 0; i < N; i++)
		nall *= 2;
	//fprintf(stderr, "nall: %ld\n", nall);
	
	for (icase = 0; icase < nall;icase++) {
		tempbit = icase;
		for (j = N-1; j >=0 ; j--) {
			LorR[j] = tempbit & 0x00000001;
			tempbit = tempbit >> 1;
		}
		//fprintf(stderr, "LorR:");
		//for (j = 0; j < N; j++) {
			//fprintf(stderr, " %d", LorR[j]);
		//}
		//fprintf(stderr, "\n");
		ix = 0;
		iy = 0;
		step = 0;
		
		for (i = 0; i < N; i++) {
			isVacantFrom[i] = 0;
		}
		gonext = 1;
		do {
			maxValueX = -1;
			maxValueY = -1;
			maxIndexX = -1;
			maxIndexY = -1;
		
			for (i = 0; i < N; i++) {
				if(isVacantFrom[Index[i]]) continue;
				temp = A[Index[i]]*(Index[i]-ix);
				if (temp > maxValueX) {
					maxValueX = temp;
					maxIndexX = Index[i];
				}
			}

			for (i = 0; i < N; i++) {
				if(isVacantFrom[Index[i]]) continue;
				temp = A[Index[i]]*(N-1-iy-Index[i]);
				if (temp > maxValueY) {
					maxValueY = temp;
					maxIndexY = Index[i];
				}
			}
	
			if (maxValueX > maxValueY) {
				if (LorR[step] != 0) gonext = 0;
				if (maxValueX < 0 || maxIndexX < 0)
					gonext = 0;
				else {
					//fprintf(stderr, "ix: %d, i: %d, ", ix, maxIndexX);
					isVacantFrom[maxIndexX] = 1;
					ix++;
					DP[ix][iy] = max(DP[ix-1][iy] + maxValueX, DP[ix][iy]);
				}

			} else if (maxValueX < maxValueY) {
				if (LorR[step] != 1) gonext = 0;
				if (maxValueY < 0 || maxIndexY <0 ) gonext = 0;
				else {
					//fprintf(stderr, "iy: %d, i: %d, ", iy, maxIndexY);
					isVacantFrom[maxIndexY] = 1;
					iy++;
					DP[ix][iy] = max(DP[ix][iy-1] + maxValueY, DP[ix][iy]);
				}
			} else if (maxValueX == maxValueY) {
				if (LorR[step] == 0){
					//fprintf(stderr, "ix: %d, i: %d, ", ix, maxIndexX);
					isVacantFrom[maxIndexX] = 1;
					ix++;
					DP[ix][iy] = max(DP[ix-1][iy] + maxValueX, DP[ix][iy]);
				} else if (LorR[step] == 1) {
					//fprintf(stderr, "iy: %d, i: %d, ", iy, maxIndexY);
					isVacantFrom[maxIndexY] = 1;
					iy++;
					DP[ix][iy] = max(DP[ix][iy-1] + maxValueY, DP[ix][iy]);
				}
			}
					
			if (gonext == 1) {
				//fprintf(stderr, "DP[%d][%d]: %ld, ",ix, iy, DP[ix][iy]);
				//fprintf(stderr, "ix: %d, iy: %d ix+iy: %d \n",ix, iy, ix+iy);
			}
			step++;
		} while (ix + iy < N && gonext == 1);
		if (step == N) {
			ixend = ix;
			iyend = iy;
		}
	}
	printf("%ld\n",DP[ixend][iyend]);
	fflush(stdout);
	free(A);
	free(Index);
	return EXIT_SUCCESS;
}