Problem:
Score : 100 points

Problem Statement

You have N cups and 1 ball.

The cups are arranged in a row, from left to right.

You turned down all the cups, then inserted the ball into the leftmost cup.

Then, you will perform the following Q operations:

The i-th operation: swap the positions of the A_i-th and B_i-th cups from the left. If one of these cups contains the ball, the ball will also move.

Since you are a magician, you can cast a magic described below:

Magic: When the ball is contained in the i-th cup from the left, teleport the ball into the adjacent cup (that is, the (i-1)-th or (i+1)-th cup, if they exist).

The magic can be cast before the first operation, between two operations, or after the last operation, but you are allowed to cast it at most once during the whole process.

Find the number of cups with a possibility of containing the ball after all the operations and possibly casting the magic.

Constraints

2 \leq N \leq 10^5

1 \leq Q \leq 10^5

1 \leq A_i < B_i \leq N

Input

The input is given from Standard Input in the following format:

N Q
A_1 B_1
A_2 B_2
:
A_Q B_Q

Output

Print the number of cups with a possibility of eventually containing the ball.

Sample Input 1

10 3
1 3
2 4
4 5

Sample Output 1

4

Sample Input 2

20 3
1 7
8 20
1 19

Sample Output 2

5

Solution in Common Lisp (SBCL 1.1.14) (judge verdict: Accepted)

;; -*- coding: utf-8 -*-
(eval-when (:compile-toplevel :load-toplevel :execute)
  (sb-int:defconstant-eqx OPT
    #+swank '(optimize (speed 3) (safety 2))
    #-swank '(optimize (speed 3) (safety 0) (debug 0))
    #'equal)
  #+swank (ql:quickload '(:cl-debug-print :fiveam) :silent t)
  #-swank (set-dispatch-macro-character
           ;; enclose the form with VALUES to avoid being captured by LOOP macro
           #\# #\> (lambda (s c p) (declare (ignore c p)) `(values ,(read s nil nil t)))))
#+swank (cl-syntax:use-syntax cl-debug-print:debug-print-syntax)
#-swank (disable-debugger) ; for CS Academy

;; BEGIN_INSERTED_CONTENTS
(declaim (ftype (function * (values fixnum &optional)) read-fixnum))
(defun read-fixnum (&optional (in *standard-input*))
  "NOTE: cannot read -2^62"
  (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))
         (q (read))
         (as (make-array q :element-type 'uint31))
         (bs (make-array q :element-type 'uint31))
         (perm-r (make-array n :element-type 'uint31))
         (perm-l (make-array n :element-type 'uint31))
         (res (make-array n :element-type 'bit :initial-element 0)))
    (dotimes (i q)
      (setf (aref as i) (- (read-fixnum) 1)
            (aref bs i) (- (read-fixnum) 1)))
    (dotimes (i n)
      (setf (aref perm-r i) i
            (aref perm-l i) i))
    #>perm-r
    #>as
    #>bs
    (dotimes (i q)
      (rotatef (aref perm-r (aref as i))
               (aref perm-r (aref bs i))))
    (let ((pos1 0))
      (dotimes (i (+ q 1))
        (setf (aref res (aref perm-r pos1)) 1)
        (when (> pos1 0)
          (setf (aref res (aref perm-r (- pos1 1))) 1))
        (when (< pos1 (- n 1))
          (setf (aref res (aref perm-r (+ pos1 1))) 1))
        (when (< i q)
          (let* ((a (aref as i))
                 (b (aref bs i)))
            (cond ((= pos1 a) (setq pos1 b))
                  ((= pos1 b) (setq pos1 a)))
            (rotatef (aref perm-r a) (aref perm-r b))))))
    (println (count 1 res))))

#-swank (main)

;;;
;;; Test and benchmark
;;;

#+swank
(defun io-equal (in-string out-string &key (function #'main) (test #'equal))
  "Passes IN-STRING to *STANDARD-INPUT*, executes FUNCTION, and returns true if
the string output to *STANDARD-OUTPUT* is equal to OUT-STRING."
  (labels ((ensure-last-lf (s)
             (if (eql (uiop:last-char s) #\Linefeed)
                 s
                 (uiop:strcat s uiop:+lf+))))
    (funcall test
             (ensure-last-lf out-string)
             (with-output-to-string (out)
               (let ((*standard-output* out))
                 (with-input-from-string (*standard-input* (ensure-last-lf in-string))
                   (funcall function)))))))

#+swank
(defun get-clipbrd ()
  (with-output-to-string (out)
    ;; (run-program "C:/Windows/System32/WindowsPowerShell/v1.0/powershell.exe" '("get-clipboard") :output out)
    (run-program "powershell.exe" '("-Command" "Get-Clipboard") :output out :search t)))

#+swank (defparameter *this-pathname* (uiop:current-lisp-file-pathname))
#+swank (defparameter *dat-pathname* (uiop:merge-pathnames* "test.dat" *this-pathname*))

#+swank
(defun run (&optional thing (out *standard-output*))
  "THING := null | string | symbol | pathname

null: run #'MAIN using the text on clipboard as input.
string: run #'MAIN using the string as input.
symbol: alias of FIVEAM:RUN!.
pathname: run #'MAIN using the text file as input."
  (let ((*standard-output* out))
    (etypecase thing
      (null
       (with-input-from-string (*standard-input* (delete #\Return (get-clipbrd)))
         (main)))
      (string
       (with-input-from-string (*standard-input* (delete #\Return thing))
         (main)))
      (symbol (5am:run! thing))
      (pathname
       (with-open-file (*standard-input* thing)
         (main))))))

#+swank
(defun gen-dat ()
  (uiop:with-output-file (out *dat-pathname* :if-exists :supersede)
    (format out "")))

#+swank
(defun bench (&optional (out (make-broadcast-stream)))
  (time (run *dat-pathname* out)))

;; To run: (5am:run! :sample)
#+swank
(it.bese.fiveam:test :sample
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "10 3
1 3
2 4
4 5
"
    "4
"))
  (it.bese.fiveam:is
   (common-lisp-user::io-equal "20 3
1 7
8 20
1 19
"
    "5
")))