One day n friends gathered together to play "Mafia". During each round of the game some player must be the supervisor and other n - 1 people take part in the game. For each person we know in how many rounds he wants to be a player, not the supervisor: the i-th person wants to play ai rounds. What is the minimum number of rounds of the "Mafia" game they need to play to let each person play at least as many rounds as they want?

Input

The first line contains integer n (3 ≤ n ≤ 105). The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 109) — the i-th number in the list is the number of rounds the i-th person wants to play.

Output

In a single line print a single integer — the minimum number of game rounds the friends need to let the i-th person play at least ai rounds.

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.

Examples

Input

3
3 2 2


Output

4


Input

4
2 2 2 2


Output

3

Note

You don't need to know the rules of "Mafia" to solve this problem. If you're curious, it's a game Russia got from the Soviet times: http://en.wikipedia.org/wiki/Mafia_(party_game).
		import java.io.BufferedReader;
	import java.io.IOException;
	import java.io.InputStream;
	import java.io.InputStreamReader;
	import java.io.PrintWriter;
	import java.util.ArrayList;
	import java.util.Arrays;
	import java.util.InputMismatchException;
	import java.util.Iterator;
	import java.util.TreeMap;
			public class Main implements Runnable
			{
				static final long MOD = 1000000007L;
				static final long MOD2 = 1000000009L;
				static class InputReader
				{
					private InputStream stream;
					private byte[] buf = new byte[1024];
					private int curChar;
					private int numChars;
					private SpaceCharFilter filter;
					private BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
			 
					public InputReader(InputStream stream)
					{
						this.stream = stream;
					}
					
					public int read()
					{
						if (numChars==-1) 
							throw new InputMismatchException();
						
						if (curChar >= numChars)
						{
							curChar = 0;
							try 
							{
								numChars = stream.read(buf);
							}
							catch (IOException e)
							{
								throw new InputMismatchException();
							}
							
							if(numChars <= 0)				
								return -1;
						}
						return buf[curChar++];
					}
				 
					public String nextLine()
					{
						String str = "";
			            try
			            {
			                str = br.readLine();
			            }
			            catch (IOException e)
			            {
			                e.printStackTrace();
			            }
			            return str;
					}
					public int nextInt()
					{
						int c = read();
						
						while(isSpaceChar(c)) 
							c = read();
						
						int sgn = 1;
						
						if (c == '-') 
						{
							sgn = -1;
							c = read();
						}
						
						int res = 0;
						do 
						{
							if(c<'0'||c>'9') 
								throw new InputMismatchException();
							res *= 10;
							res += c - '0';
							c = read();
						}
						while (!isSpaceChar(c)); 
						
						return res * sgn;
					}
					
					public long nextLong() 
					{
						int c = read();
						while (isSpaceChar(c))
							c = read();
						int sgn = 1;
						if (c == '-') 
						{
							sgn = -1;
							c = read();
						}
						long res = 0;
						
						do 
						{
							if (c < '0' || c > '9')
								throw new InputMismatchException();
							res *= 10;
							res += c - '0';
							c = read();
						}
						while (!isSpaceChar(c));
							return res * sgn;
					}
					
					public double nextDouble() 
					{
						int c = read();
						while (isSpaceChar(c))
							c = read();
						int sgn = 1;
						if (c == '-') 
						{
							sgn = -1;
							c = read();
						}
						double res = 0;
						while (!isSpaceChar(c) && c != '.') 
						{
							if (c == 'e' || c == 'E')
								return res * Math.pow(10, nextInt());
							if (c < '0' || c > '9')
								throw new InputMismatchException();
							res *= 10;
							res += c - '0';
							c = read();
						}
						if (c == '.') 
						{
							c = read();
							double m = 1;
							while (!isSpaceChar(c)) 
							{
								if (c == 'e' || c == 'E')
									return res * Math.pow(10, nextInt());
								if (c < '0' || c > '9')
									throw new InputMismatchException();
								m /= 10;
								res += (c - '0') * m;
								c = read();
							}
						}
						return res * sgn;
					}
					
					public String readString() 
					{
						int c = read();
						while (isSpaceChar(c))
							c = read();
						StringBuilder res = new StringBuilder();
						do 
						{
							res.appendCodePoint(c);
							c = read();
						} 
						while (!isSpaceChar(c));
						
						return res.toString();
					}
				 
					public boolean isSpaceChar(int c) 
					{
						if (filter != null)
							return filter.isSpaceChar(c);
						return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
					}
				 
					public String next() 
					{
						return readString();
					}
					
					public interface SpaceCharFilter 
					{
						public boolean isSpaceChar(int ch);
					}
				}
			 	
				public static void main(String args[]) throws Exception
				{
					new Thread(null, new Main(),"Main",1<<26).start();
				}
				int MAXN = 100001;
				ArrayList<Integer> adj[];
				int V;
				public void run() 
				{
					InputReader sc= new InputReader(System.in);
					PrintWriter w= new PrintWriter(System.out);
					int n = sc.nextInt();
					int[] arr=  new int[n];
					long sum = 0;
					long max = Integer.MIN_VALUE;
					for(int i = 0;i < n;i++) {
						arr[i] = sc.nextInt();
						sum += arr[i];
						max = Math.max(max,arr[i]);
					}
					w.println(Math.max(max,(sum + n - 2)/(n-1)));
					w.close();
				}
				int bsearch(int[] ar,int val,int[] arr,int length){
					int l = 0;
					int r = length-1;
					int ans = -1;
					while(l <= r) {
						int mid = (l + r)/2;
						if(arr[ar[mid]] >= val) {
							ans = mid;
							r = mid - 1;
						}else {
							l = mid + 1;
						}
					}
					if(ans == -1) {
						return length;
					}
					return ans;
				}
				boolean[] visited;
				void dfs(int a) {
					visited[a] = true;
					Iterator<Integer> it = adj[a].iterator();
					while(it.hasNext()) {
						int x = it.next();
						if(!visited[x]) {
							dfs(x);
						}
					}
				}
				int cnt=  0;
				void dfsUtil(int a,boolean[] visit) {
					visit[a] = true;
					Iterator<Integer> it = adj[a].iterator();
					while(it.hasNext()) {
						int x = it.next();
						if(!visit[x]) {
							cnt++;
							dfsUtil(x,visit);
						}
					}
				}
				
				String reverse(String a) {
					String navi = "";
					for(int i = a.length()-1;i >= 0;i--) {
						navi += a.charAt(i);
					}
					return navi;
				}
				static boolean isPrime(long n)
			    {
			        // Corner cases
			        if (n <= 1) return false;
			        if (n <= 3) return true;
			     
			        // This is checked so that we can skip 
			        // middle five numbers in below loop
			        if (n % 2 == 0 || n % 3 == 0) return false;
			     
			        for (int i = 5; i * i <= n; i = i + 6)
			            if (n % i == 0 || n % (i + 2) == 0)
			            return false;
			     
			        return true;
			    }
			 
				long count = 0;
				long[][] dist;
				void flydwarShall(int k,int size) {
					for(int i = 0;i < size;i++) {
						for(int j = 0;j < size;j++) {
							if(dist[i][j] > dist[i][k] + dist[k][j]) {
								dist[i][j] = dist[i][k] + dist[k][j];
							}
						}
					}
				}
				Pair[] segTree;
				int[] arr;
				void build(int l,int r,int pos) {
					if(l == r) {
						segTree[pos] = new Pair(1,1,1,arr[l],arr[l],true);
						return;
					}
					int mid = (l + r) >> 1;
					build(l,mid,2*pos+1);
					build(mid+1, r, 2*pos+2);
					segTree[pos] = merge(segTree[2*pos+1], segTree[2*pos+2]);
				}
				Pair merge(Pair p1,Pair p2) {
					if(p1.val1 == 0) {
						return p2;
					}else if(p2.val1 == 0) {
						return p1;
					}
					Pair navi = new Pair();
					navi.val1 = p1.val1;
					navi.val2 = p2.val2;
					if(p1.val2 == p2.val1) {
						navi.max = Math.max(p1.max,p2.max);
						navi.first = p1.first;
						navi.second = p2.second;
						navi.whole = false;
					}else {
						navi.max = Math.max(p1.max,Math.max(p2.max,p1.second + p2.first));
						if(p1.whole && p2.whole) {
							navi.first = p1.first + p2.first;
							navi.second = p1.first + p2.first;
							navi.whole = true;
						}else if(p1.whole) {
							navi.first = p1.first + p2.first;
							navi.second = p2.second;
							navi.whole = false;
						}else if(p2.whole) {
							navi.first = p1.first;
							navi.second = p1.second + p2.first;
							navi.whole = false;
						}else {
							navi.first = p1.first;
							navi.second = p2.second;
							navi.whole = false;
						}
					}
					return navi;
				}
				Pair query(int pos, int l, int r, int start, int end)
				{
				    if(end < l || r < start)
				    {
				        return new Pair(0,0,0,0,0,false);
				    }
				    if(start <= l && r <= end)
				    {
				        // range represented by a node is completely inside the given range
				        return segTree[pos];
				    }
				    // range represented by a node is partially inside and partially outside the given range
				    int mid = (l + r) / 2;
				    Pair p1 = query(2*pos + 1, l, mid, start, end);
				    Pair p2 = query(2*pos+2, mid+1, r, start, end);
				    return merge(p1, p2);
				}
				int bsearch(Integer[] arr,int l,int r,int val) {
					int ind = -1;
					while(l <= r) {
						int mid = (l + r)/2;
						if(arr[mid] <= val) {
							l = mid + 1;
							ind = mid;
						}else {
							r = mid - 1;
						}
					}
					return ind;
				}
				
				
				long modExpo(long a,long pow,long mod) {
					long res = 1;
					while(pow > 0) {
						if(pow % 2 == 1) {
							res = (res * a) % mod;
						}
						pow = pow/2;
						a = (a * a) % mod;
					}
					return res;
				}
				  static long modInverse(long a, long m)
				    {
				        
				       
				            // If a and m are relatively prime, then modulo inverse
				            // is a^(m-2) mode m
				         
				                        return        power(a, m - 2, m);
				        
				    }
				     
				    // To compute x^y under modulo m
				// Iterative Java program to 
				// compute modular power
				
				    static long power(long x, long y,long p)
				    {
				        // Initialize result
				        long res = 1;     
				        
				        // Update x if it is more  
				        // than or equal to p
				        x = x % p; 
				     
				        while (y > 0)
				        {
				            // If y is odd, multiply x
				            // with result
				            if((y & 1)==1)
				                res = (res * x) % p;
				     
				            // y must be even now
				            // y = y / 2
				            y = y >> 1; 
				            x = (x * x) % p; 
				        }
				        return res;
				    }
				static class Temp implements Comparable<Temp>{
					String a;
					int b;
					Temp(String a,int b){
						this.a = a;
						this.b = b;
					}
					@Override
					public int compareTo(Temp t){
						return Integer.compare(t.b,this.b);
					}
				}
				static class Pair implements Comparable<Pair>{
					int first;
					int max;
					int second;
					int val1;
					int val2;
					boolean whole;
					
					Pair (int a,int b,int c,int val1,int val2,boolean whole){
						this.first = a;
						this.max = b;
						this.second = c;
						this.val1= val1;
						this.val2 = val2;
						this.whole = whole;
					}
					Pair(){
						
					}
					public boolean equals(Object o)
					{
						Pair p = (Pair)o;
						return (p.first==first && p.max==max) || (p.first == max && p.first == max);
					}
					public int hashCode()
					{
						return new Long(first).hashCode()*31 + new Long(max).hashCode();
					}
					public int compareTo(Pair p){
						return Long.compare(p.first,this.first);
					}
				}
			
			}