Problem:
Score : 300 points

Problem Statement

You are given a sequence of length N: A_1, A_2, ..., A_N.
For each integer i between 1 and N (inclusive), answer the following question:

Find the maximum value among the N-1 elements other than A_i in the sequence.

Constraints

2 \leq N \leq 200000

1 \leq A_i \leq 200000

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1
:
A_N

Output

Print N lines. The i-th line (1 \leq i \leq N) should contain the maximum value among the N-1 elements other than A_i in the sequence.

Sample Input 1

3
1
4
3

Sample Output 1

4
3
4

The maximum value among the two elements other than A_1, that is, A_2 = 4 and A_3 = 3, is 4.

The maximum value among the two elements other than A_2, that is, A_1 = 1 and A_3 = 3, is 3.

The maximum value among the two elements other than A_3, that is, A_1 = 1 and A_2 = 4, is 4.

Sample Input 2

2
5
5

Sample Output 2

5
5

Solution in Common Lisp (SBCL 1.1.14) (judge verdict: Wrong Answer)

;; -*- coding: utf-8 -*-
(eval-when (:compile-toplevel :load-toplevel :execute)
  (defparameter OPT
    #+swank '(optimize (speed 3) (safety 2))
    #-swank '(optimize (speed 3) (safety 0) (debug 0)))
  #+swank (ql:quickload '(:cl-debug-print :fiveam))
  #-swank (set-dispatch-macro-character #\# #\> (lambda (s c p) (declare (ignore c p)) (read s nil (values) t))))
#+swank (cl-syntax:use-syntax cl-debug-print:debug-print-syntax)
#-swank (disable-debugger) ; for CS Academy

;; BEGIN_INSERTED_CONTENTS
;;;
;;; Disjoint sparse table
;;;

;;; Reference:
;;; https://discuss.codechef.com/questions/117696/tutorial-disjoint-sparse-table
;;; http://noshi91.hatenablog.com/entry/2018/05/08/183946 (Japanese)
;;; http://drken1215.hatenablog.com/entry/2018/09/08/162600 (Japanese)

(declaim (inline make-disjoint-sparse-table))
(defun make-disjoint-sparse-table (vector binop)
  (let* ((n (length vector))
         (height (integer-length (- n 1)))
         (table (make-array (list height n) :element-type '(unsigned-byte 32))))
    (dotimes (j n)
      (setf (aref table 0 j) (aref vector j)))
    (do ((i 1 (+ i 1)))
        ((>= i height))
      (let* ((width/2 (ash i 1))
             (width (* width/2 2)))
        (do ((j 0 (+ j width)))
            ((>= j n))
          (let ((mid (min (+ j width/2) n)))
            ;; fill the first half
            (setf (aref table i (- mid 1))
                  (aref vector (- mid 1)))
            (do ((k (- mid 2) (- k 1)))
                ((< k j))
              (setf (aref table i k)
                    (funcall binop (aref vector k) (aref table i (+ k 1)))))
            (when (>= mid n)
              (return))
            ;; fill the second half
            (setf (aref table i mid)
                  (aref vector mid))
            (let ((end (min n (+ mid width/2))))
              (do ((k (+ mid 1) (+ k 1)))
                  ((>= k end))
                (setf (aref table i k)
                      (funcall binop (aref table i (- k 1)) (aref vector k)))))))))
    table))

(declaim (inline dst-query))
(defun dst-query (table binop left right)
  "Queries the interval [LEFT, RIGHT). Note that a null interval [x, x) is not
allowed as disjoint sparse table deals with a semigroup."
  (declare ((integer 0 #.most-positive-fixnum) left right)
           ((simple-array (unsigned-byte 32) (* *)) table))
  (assert (< left right))
  (setq right (- right 1)) ;; change to closed interval
  (if (= left right)
      (aref table 0 left)
      (let ((h (- (integer-length (logxor left right)) 1)))
        (funcall binop
                 (aref table h left)
                 (aref table h right)))))

(defmacro with-buffered-stdout (&body body)
  "Buffers all outputs to *STANDARD-OUTPUT* in BODY and flushes them to
*STANDARD-OUTPUT* after BODY has been done (without error). Note that only
BASE-CHAR is allowed."
  (let ((out (gensym)))
    `(let ((,out (make-string-output-stream :element-type 'base-char)))
       (let ((*standard-output* ,out))
         ,@body)
       (write-string (get-output-stream-string ,out)))))

(declaim (ftype (function * (values fixnum &optional)) read-fixnum))
(defun read-fixnum (&optional (in *standard-input*))
  (declare #.OPT)
  (macrolet ((%read-byte ()
               `(the (unsigned-byte 8)
                     #+swank (char-code (read-char in nil #\Nul))
                     #-swank (sb-impl::ansi-stream-read-byte in nil #.(char-code #\Nul) nil))))
    (let* ((minus nil)
           (result (loop (let ((byte (%read-byte)))
                           (cond ((<= 48 byte 57)
                                  (return (- byte 48)))
                                 ((zerop byte) ; #\Nul
                                  (error "Read EOF or #\Nul."))
                                 ((= byte #.(char-code #\-))
                                  (setf minus t)))))))
      (declare ((integer 0 #.most-positive-fixnum) result))
      (loop
        (let* ((byte (%read-byte)))
          (if (<= 48 byte 57)
              (setq result (+ (- byte 48) (* 10 (the (integer 0 #.(floor most-positive-fixnum 10)) result))))
              (return (if minus (- result) result))))))))

(defmacro dbg (&rest forms)
  #+swank
  (if (= (length forms) 1)
      `(format *error-output* "~A => ~A~%" ',(car forms) ,(car forms))
      `(format *error-output* "~A => ~A~%" ',forms `(,,@forms)))
  #-swank (declare (ignore forms)))

(defmacro define-int-types (&rest bits)
  `(progn
     ,@(mapcar (lambda (b) `(deftype ,(intern (format nil "UINT~A" b)) () '(unsigned-byte ,b))) bits)
     ,@(mapcar (lambda (b) `(deftype ,(intern (format nil "INT~A" b)) () '(signed-byte ,b))) bits)))
(define-int-types 2 4 7 8 15 16 31 32 62 63 64)

(declaim (inline println))
(defun println (obj &optional (stream *standard-output*))
  (let ((*read-default-float-format* 'double-float))
    (prog1 (princ obj stream) (terpri stream))))

(defconstant +mod+ 1000000007)

;; Body

(defun main ()
  (let* ((n (read))
         (as (make-array n :element-type 'uint32)))
    (dotimes (i n)
      (setf (aref as i) (read-fixnum)))
    (let ((table (make-disjoint-sparse-table as #'max)))
      (with-buffered-stdout
        (dotimes (i n)
          (println (max (if (zerop i)
                            0
                            (dst-query table #'max 0 i))
                        (if (= (+ i 1) n)
                            0
                            (dst-query table #'max (+ i 1) n)))))))))

#-swank (main)