255 and 256

The output is count = 255

We did write 256 characters, Why do we only get 255 of them?

#include <stdio.h>

int main(void)

{

  FILE *fp;

  char c;

  int count;

  int i;

  fp = fopen("file", "wb");

  for (i = 0; i < 256; i++)

    fputc(i, fp);

  fclose(fp);

  fp = fopen("file", "rb");

  count = 0;

  while ((c = fgetc(fp)) != EOF)

    count++;

  printf("count = %d\n", count);

  return 0;

}