Alice and Bob begin their day with a quick game. They first choose a starting number X0 ≥ 3 and try to reach one million by the process described below. 

Alice goes first and then they take alternating turns. In the i-th turn, the player whose turn it is selects a prime number smaller than the current number, and announces the smallest multiple of this prime number that is not smaller than the current number.

Formally, he or she selects a prime p < Xi - 1 and then finds the minimum Xi ≥ Xi - 1 such that p divides Xi. Note that if the selected prime p already divides Xi - 1, then the number does not change.

Eve has witnessed the state of the game after two turns. Given X2, help her determine what is the smallest possible starting number X0. Note that the players don't necessarily play optimally. You should consider all possible game evolutions.

Input

The input contains a single integer X2 (4 ≤ X2 ≤ 106). It is guaranteed that the integer X2 is composite, that is, is not prime.

Output

Output a single integer — the minimum possible X0.

Examples

Input

14


Output

6


Input

20


Output

15


Input

8192


Output

8191

Note

In the first test, the smallest possible starting number is X0 = 6. One possible course of the game is as follows: 

  * Alice picks prime 5 and announces X1 = 10
  * Bob picks prime 7 and announces X2 = 14. 



In the second case, let X0 = 15. 

  * Alice picks prime 2 and announces X1 = 16
  * Bob picks prime 5 and announces X2 = 20. 
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStreamWriter;
import java.math.BigDecimal;
import java.math.MathContext;
import java.math.RoundingMode;


import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Map.Entry;
import java.util.PriorityQueue;
import java.util.Random;
import java.util.TreeSet;


public final class CF_VK_2018_R1_A{

	static boolean verb=true;
	static void log(Object X){if (verb) System.err.println(X);}
	static void log(Object[] X){if (verb) {for (Object U:X) System.err.print(U+" ");System.err.println("");}}
	static void log(int[] X){if (verb) {for (int U:X) System.err.print(U+" ");System.err.println("");}}
	static void log(int[] X,int L){if (verb) {for (int i=0;i<L;i++) System.err.print(X[i]+" ");System.err.println("");}}
	static void log(long[] X){if (verb) {for (long U:X) System.err.print(U+" ");System.err.println("");}}

	static void logWln(Object X){if (verb) System.err.print(X);}
	static void info(Object o){	System.out.println(o);}
	static void output(Object o){outputWln(""+o+"\n");	}
	static void outputWln(Object o){try {out.write(""+ o);} catch (Exception e) {}}


	//static long mod=1000000007;
	static long mod=998244353;
	static long MX=1000000000000000001L;

	// Global vars
	static BufferedWriter out;
	static InputReader reader;

	static long powerMod(long b,long e,long m){
		long x=1;
		while (e>0) {
			if (e%2==1)
				x=(b*x)%m;
			b=(b*b)%m;
			e=e/2;
		}
		return x; 
	}



	static int findBiggest(int x,int[] mem,boolean notTooBig){
		int big=1;
		int p=mem[x];
		if (x-p+1>=p)
			big=p;
		return big;
	}
	
	/*
	static int findBiggest(int x,int[] mem,boolean notTooBig){
		int big=1;
		int y=x;
		while (mem[y]!=0){
			int p=mem[y];
			if (p>big) {
				if (notTooBig && x-p+1>=p)
					big=p;
				if (!notTooBig)
					big=p;
			}
			y/=p;
			if (big>1)
				return big;
		}
		return big;
	}
	*/

	static void process() throws Exception {


		out = new BufferedWriter(new OutputStreamWriter(System.out));
		reader=new InputReader(System.in);


		int MAX=1000001;
		int[] mem=new int[MAX];

		for (int i=2;i<MAX;i++){
			if (mem[i]==0){
				int j=i;
				while (j<MAX){
					mem[j]=i;
					j+=i;
				}
			}
		}
		int n=reader.readInt();

		int[] src=new int[n+1];
		ArrayList<Integer> cand=new ArrayList<Integer>();

		int target=n;
		for (int i=0;i<=n;i++)
			src[i]=i;


		// new try
		ArrayList<Integer> lst=new ArrayList<Integer>();
		int big=findBiggest(n,mem,true);
		//log("big:"+big);


		int min=n;
		for (int m=n-big+1;m<=n;m++){
			int tm=findBiggest(m,mem,true);
			
			min=Math.min(min,m-tm+1);

		}
		target=min;


		/*
		//too slow
		for (int x=3;x<=n;x++){
			lp:for (int p:primes){
				if (p>x)
					break lp;
				int y=(x/p)*p;
				if (y<x)
					y+=p;
				if (y<=n){
					if (src[y]>x)
						src[y]=x;
				}
				if (y==n){
					if (src[x]<target)
						target=src[x];
				}
			}

		}
		 */
		output(target);



		try {
			out.close();
		}
		catch (Exception EX){}


	}


	public static void main(String[] args) throws Exception {
		process();

	}

	static final class InputReader {
		private final InputStream stream;
		private final byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

		public InputReader(InputStream stream) {
			this.stream = stream;
		}

		private int read() throws IOException {
			if (curChar >= numChars) {
				curChar = 0;
				numChars = stream.read(buf);
				if (numChars <= 0) {
					return -1;
				}
			}
			return buf[curChar++];
		}


		public final String readString() throws IOException {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			StringBuilder res=new StringBuilder();
			do {
				res.append((char)c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public final int readInt() throws IOException {
			int c = read();
			boolean neg=false;
			while (isSpaceChar(c)) {
				c = read();
			}
			char d=(char)c;
			//log("d:"+d);
			if (d=='-') {
				neg=true;
				c = read();
			}
			int res = 0;
			do {
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			//log("res:"+res);
			if (neg)
				return -res;
			return res;

		}

		public final long readLong() throws IOException {
			int c = read();
			boolean neg=false;
			while (isSpaceChar(c)) {
				c = read();
			}
			char d=(char)c;
			//log("d:"+d);
			if (d=='-') {
				neg=true;
				c = read();
			}
			long res = 0;
			do {
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			//log("res:"+res);
			if (neg)
				return -res;
			return res;

		}




		private boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
	}


}