Problem:
Score : 200 points

Problem Statement

Determine if an N-sided polygon (not necessarily convex) with sides of length L_1, L_2, ..., L_N can be drawn in a two-dimensional plane.

You can use the following theorem:

Theorem: an N-sided polygon satisfying the condition can be drawn if and only if the longest side is strictly shorter than the sum of the lengths of the other N-1 sides.

Constraints

All values in input are integers.

3 \leq N \leq 10

1 \leq L_i \leq 100

Input

Input is given from Standard Input in the following format:

N
L_1 L_2 ... L_N

Output

If an N-sided polygon satisfying the condition can be drawn, print Yes; otherwise, print No.

Sample Input 1

4
3 8 5 1

Sample Output 1

Yes

Since 8 < 9 = 3 + 5 + 1, it follows from the theorem that such a polygon can be drawn on a plane.

Sample Input 2

4
3 8 4 1

Sample Output 2

No

Since 8 \geq 8 = 3 + 4 + 1, it follows from the theorem that such a polygon cannot be drawn on a plane.

Sample Input 3

10
1 8 10 5 8 12 34 100 11 3

Sample Output 3

No

Solution in C (GCC 5.4.1) (judge verdict: Runtime Error)

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

#define BUF_SIZE 2048

static void calc(int n, int sides_count, int *sides);

int main() {
  char buf[BUF_SIZE];
  int n;
  int sides[100];
  char *tmp_side;
  int sides_count = 0;
  if(fgets(buf, sizeof buf, stdin)) {
    n = atoi(buf);
  }
  if(fgets(buf, sizeof buf, stdin) == NULL) {
    exit(1);
  }

  tmp_side = malloc(sizeof(char) * 100);
  for(int i = 0; i < sizeof buf; i++) {
    if(buf[i] == '\0') break;
    if(isspace(buf[i])) {
      int result = atoi(tmp_side);
      sides[sides_count] = result;
      tmp_side[0] = '\0';
      sides_count++;
    } else {
      strcat(tmp_side, &buf[i]);
    }
  }
  calc(n, sides_count, sides);
}

void calc(int n, int sides_count, int *sides) {
  int max_index = 0;
  int max = 0;
  int sum;
  if(n < 3 || n > 10) {
    printf("No");
    exit(1);
  }
  for(int i = 0; i < sizeof(sides); i++) {
    if(sides[i] > max) {
      max = sides[i];
      max_index = i;
    }
    if(sides[i] < 1 && sides[i] > 100) {
      printf("No");
      exit(1);
    }
  }
  for(int i = 0; i < sizeof(sides); i++) {
    if(i != max_index) {
      sum += sides[i];
    }
  }
  if(max >= sum) {
    printf("No");
  } else {
    printf("Yes");
  }
}