/*
import java.util.*;
class Main{
public static void main(String[] args) {
System.out.println("Hello");
}
}
*/
/*
import java.util.*;
class Main{
public static void main(String[] args) {
System.out.println("Hello World");
}
}
*/
/*
import java.util.*;
class Main{
public static void main(String[] args) {
System.out.println("Hello");
System.out.println("World");
}
}
*/
/*
import java.util.*;
class Main{
public static void main(String[] args) {
System.out.println("'Hello'");
}
}
*/
/*
import java.util.*;
class Main{
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int a = sc.nextInt();
System.out.println(a+" "+a+" "+a); }
}
*/
/*
import java.util.*;
class Main{
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int a = sc.nextInt();
int b = sc.nextInt();
System.out.println(a+"+"+b+"="+(a+b));
System.out.println(a+"-"+b+"="+(a-b));
System.out.println(a+"*"+b+"="+(a*b));
System.out.println(a+"/"+b+"="+(a/b));
}
}
*/
/*
import java.util.*;
class Main{
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int a = sc.nextInt();
int b = sc.nextInt();
System.out.println(a*b/2.0);
}
}
/*
import java.util.*;
class Main{
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int a = sc.nextInt();
if(a%7==0) System.out.println("multiple");
else System.out.println("not multiple");
}
}
*/
/*
import java.util.*;
class Main{
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int a = sc.nextInt();
int b = sc.nextInt();
int c = sc.nextInt();
if(a>170 && b>170 && c>170) System.out.println("PASS");
else System.out.println("CRASH");
}
}
*/
/*
import java.util.*;
class Main{
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int n =sc.nextInt();
n=2*(n/10)+20*(n%10);
if(n>99) n=n%100;
System.out.println(n);
if(n>50) System.out.println("OH MY GOD");
else System.out.println("GOOD");
}
}
*/
/*
import java.util.*;
class Main{
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int a = sc.nextInt();
int b = sc.nextInt();
if(a%b==0) System.out.println(b+"*"+(a/b)+"="+a);
else if(b%a==0) System.out.println(a+"*"+(b/a)+"="+b);
else System.out.println("none");
}
}
*/
/*
import java.util.*;
class Main{
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int a = sc.nextInt();
int b = sc.nextInt();
int s=0;
for(int i=a;i<=b;i++) {
if(i%3==0) s+=i;
}
System.out.println(s);
}
}
*/
/*
import java.util.*;
class Main{
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
int s=0;
for(int i=0;i<n;i++) {
int a = sc.nextInt();
if(a%5==0) s+=a;
}
System.out.println(s);
}
}
*/
/*
import java.util.*;
class Main{
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int a = sc.nextInt();
int c=0;
for(int i=2;i*i<=a;i++) {
if(a%i==0) {
c=1;
break;
}
}
if(c==0) System.out.println("prime");
else System.out.println("not prime");
}
}
*/
/*
import java.util.*;
class Main{
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int a = sc.nextInt();
int b = sc.nextInt();
int s=0;
for(int i=a;i<=b;i++) {
if(i%2==0) s-=i;
else s+=i;
}
System.out.println(s);
}
}
*/
/*
import java.util.*;
class Main{
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int max=-1000000,min=1000000;
for(int i=0;i<5;i++) {
int a = sc.nextInt();
if(a>max) max=a;
if(a<min) min=a;
}
System.out.println(max);
System.out.println(min);
}
}
*/
/*
import java.util.*;
class Main{
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int a = sc.nextInt();
int b = sc.nextInt();
for(int i=a;i<=b;i++) {
for(int j=1;j<10;j++) {
System.out.println(i+"*"+j+"="+(i*j));
}
}
}
}
*/
/*
import java.util.*;
class Main{
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
for(int i=n;i>0;i--) {
for(int j=n-i;j>0;j--) {
System.out.print(" ");
}
for(int j=i;j>0;j--) {
System.out.print("*");
}
System.out.print("\n");
}
}
}
*/
/*
import java.util.*;
class Main{
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
for(int i=1;i<=n;i++) {
for(int j=n-i;j>0;j--) {
System.out.print(" ");
}
for(int j=0;j<n;j++) {
System.out.print("*");
}
System.out.print("\n");
}
}
}
문자열 != 문자일차원배열
문자열끼리의 비교는 equals로
문자끼리는 == 가능
import java.util.*;
class Main{
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
//String str = sc.next();
//String str1 = str.replace('e', 'o');
//String str1 = str.substring(3, 6);
//String str1 = str.toLowerCase();
//String str = "a hello ";
//System.out.println(str);
//String str1 = str.trim(); //문자열의 맨 앞이나 맨 뒤에 있는 공백들 제거
//System.out.println(str1);
//if(str.equals("hello"))
//char[] str1 = str.toCharArray();
//for(int i=0;i<str.length();i++) {
//if(str.charAt(i)=='t')
//System.out.println(str.charAt(i));
//}
//배열
//int arr[50]= {1,2,3,4,5}; (x)
// int[] arr = new int[50]; //일차원 배열 선언
// int n = sc.nextInt();
// float[] arrf = new float[n]; //변수갯수로도 선언 가능!!
//
// System.out.println(arr[10]);
//
// int[][] arr = new int[50][50]; //이차원 배열 선언
String str = "aello";
System.out.println((char)(str.charAt(0)+10));
}
}
*/
/*
import java.util.*;
class Main{
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
String str = sc.next();
for(int i=0;i<str.length();i++) {
System.out.println("'"+str.charAt(i)+"'");
}
}
}
*/
/*
import java.util.*;
class Main{
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int[][] arr = new int[101][101];
int h = sc.nextInt();
int w = sc.nextInt();
int n = sc.nextInt();
for(int i=0;i<n;i++) {
int l = sc.nextInt();
int d = sc.nextInt();
int x = sc.nextInt();
int y = sc.nextInt();
if(d==0) {
for(int j=y;j<y+l;j++) {
arr[x][j]=1;
}
}
else {
for(int j=x;j<x+l;j++) {
arr[j][y]=1;
}
}
}
for(int i=1;i<=h;i++) {
for(int j=1;j<=w;j++) {
System.out.print(arr[i][j]+" ");
}
System.out.print("\n");
}
}
}
*/
/*
import java.util.*;
class Main{
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int[][] arr = new int[11][11];
for(int i=0;i<10;i++)
for(int j=0;j<10;j++)
arr[i][j] = sc.nextInt();
int x=1,y=1;
while(arr[x][y]==0) {
arr[x][y]=9;
if(arr[x][y+1]!=1) {
y++;
if(arr[x][y]==2) break;
}
else if(arr[x+1][y]!=1) {
x++;
if(arr[x][y]==2) break;
}
}
arr[x][y]=9;
for(int i=0;i<10;i++) {
for(int j=0;j<10;j++)
System.out.print(arr[i][j]+" ");
System.out.print("\n");
}
}
}
*/
/*
import java.util.*;
class Main{
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
String str = sc.next();
for(int i=0;i<str.length();i++) {
if(str.charAt(i)>64 && str.charAt(i)<91) System.out.print((char)(str.charAt(i)+32));
else if(str.charAt(i)>96 && str.charAt(i)<123) System.out.print((char)(str.charAt(i)-32));
else System.out.print((char)(str.charAt(i)));
}
}
}
*/
/*
import java.util.*;
class Main{
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
int[] arr = new int[n];
int i,j;
for(i=0;i<n;i++) {
arr[i] = sc.nextInt();
}
for(i=0;i<n;i++) {
for(j=i;j<n;j++) {
System.out.print(arr[j]+" ");
}
for(j=0;j<i;j++) {
System.out.print(arr[j]+" ");
}
System.out.print("\n");
}
}
}
*/
/*
import java.util.*;
class Main{
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
String str = sc.nextLine();
for(int i=0;i<str.length();i++) {
if(str.charAt(i)!=' ') System.out.print(str.charAt(i));
}
}
}
*/
/*
import java.util.*;
class Main{
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
String str = sc.next();
for(int i=0;i<str.length();i++) {
if(str.charAt(i)=='t') System.out.print((i+1)+" ");
}
}
}
*/
/*
import java.util.*;
class Main{
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
int[][] arr = new int[n+1][n+1];
for(int i=0;i<n;i++) {
arr[i][0] = sc.nextInt();
}
for(int i=0;i<n;i++) {
for(int j=0;j<=i;j++) {
if(j!=0) arr[i][j]=arr[i][j-1]-arr[i-1][j-1];
System.out.print(arr[i][j]+" ");
}
System.out.print("\n");
}
}
}
*/
/*
import java.util.*;
class Main{
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int[][] arr = new int[12][11];
int check=0;
for(int i=0;i<11;i++)
for(int j=0;j<10;j++)
arr[i][j] = sc.nextInt();
for(int j=0;j<10;j++) {
if(arr[10][j]==0) continue;
check=0;
for(int i=9;i>=0;i--) {
if(arr[i][j]>0) {
check=1;
break;
}
else if(arr[i][j]<0) {
check=-1;
break;
}
}
if(check==0) System.out.println((j+1)+" "+"safe");
else if(check==1) System.out.println((j+1)+" "+"crash");
else System.out.println((j+1)+" "+"fall");
}
}
}
*/
/*
import java.util.*;
class Main{
public static void main(String[] args) {
Scanner sc = new Scanner(System.in);
int n = sc.nextInt();
int[][] arr = new int[n+1][n+1];
int x=1,y=(n+1)/2;
for(int i=1;i<=n*n;i++) {
if(x>n) x-=n;
else if(x<1) x+=n;
if(y>n) y-=n;
arr[x][y]=i;
if(i%n==0) x++;
else {
x--;
y++;
}
}
for(int i=1;i<=n;i++) {
for(int j=1;j<=n;j++) System.out.print(arr[i][j]+" ");
System.out.print("\n");
}
}
}
*/