Simple code isnt working like it should

I have some problems with a simple program. The purpose of the program is to determine whether a user entered character is a number or a letter. Whats wrong with this code? The first part before the && seems to work but the second part, after the &&. I would really appreciate some help.

int main()
{
    char input = '0';
    printf("Enter a letter or a number: ");
    scanf("%c", &input);

    if((input >= '0') && (input <= '9'))
    {
        printf("The input is a number.\n");
    }
        else if((input >= 'A' && input <= 'Z') || (input >= 'a' && input <= 'z'))
    {
        printf("The input is a letter.\n");
    }
    else
    {
        printf("The input is not a number or a letter.\n");
    }
    return 0;
}