static int LowerInsertionPoint ( int arr [ ] , int n , int X ) {
  if ( X < arr [ 0 ] ) return 0 ;
  else if ( X > arr [ n - 1 ] ) return n ;
  int lowerPnt = 0 ;
  int i = 1 ;
  while ( i < n && arr [ i ] < X ) {
    lowerPnt = i ;
    i = i * 2 ;
  }
  while ( lowerPnt < n && arr [ lowerPnt ] < X ) lowerPnt ++ ;
  return lowerPnt ;
}

static int LowerInsertionPoint ( int arr [ ] , int n , int X ) { if ( X < arr [ 0 ] ) return 0 ; else if ( X > arr [ n - 1 ] ) return n ; int lowerPnt = 0 ; int i = 1 ; while ( i < n && arr [ i ] < X ) { lowerPnt = i ; i = i * 2 ; } while ( lowerPnt < n && arr [ lowerPnt ] < X ) lowerPnt ++ ; return lowerPnt ; }
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