private static int lower_bound ( long [ ] a , int low , int high , int element ) {
  while ( low < high ) {
    int middle = low + ( high - low ) / 2 ;
    if ( element > a [ middle ] ) low = middle + 1 ;
    else high = middle ;
  }
  return low ;
}

private static int lower_bound ( long [ ] a , int low , int high , int element ) { while ( low < high ) { int middle = low + ( high - low ) / 2 ; if ( element > a [ middle ] ) low = middle + 1 ; else high = middle ; } return low ; }
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