static int magicIndex ( int arr [ ] , int start , int end ) {
  if ( start > end ) return - 1 ;
  int midIndex = ( start + end ) / 2 ;
  int midValue = arr [ midIndex ] ;
  if ( midIndex == midValue ) return midIndex ;
  int left = magicIndex ( arr , start , Math . min ( midValue , midIndex - 1 ) ) ;
  if ( left >= 0 ) return left ;
  return magicIndex ( arr , Math . max ( midValue , midIndex + 1 ) , end ) ;
}

static int magicIndex ( int arr [ ] , int start , int end ) { if ( start > end ) return - 1 ; int midIndex = ( start + end ) / 2 ; int midValue = arr [ midIndex ] ; if ( midIndex == midValue ) return midIndex ; int left = magicIndex ( arr , start , Math . min ( midValue , midIndex - 1 ) ) ; if ( left >= 0 ) return left ; return magicIndex ( arr , Math . max ( midValue , midIndex + 1 ) , end ) ; }
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