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 javax.swing.plaf.basic.BasicTreeUI;
import java.io.*;
import java.lang.reflect.Array;
import java.math.BigInteger;
import java.util.*;


public class Main {
    private static Scanner sc;
    private static Printer pr;
    static boolean []visited;
    static int []color;
    static int []pow=new int[(int)3e5+1];
    static int []count;
    static boolean check=true;
    static boolean checkBip=true;
    static TreeSet<Integer>[]list;
    private static long aLong=(long)(Math.pow(10,9)+7);
    static final long div=998244353;
    static  int answer=0;
    static int[]countSubTree;
    static int[]colorNode;
    static boolean con=true;
    static ArrayList<Integer>dfsPath=new ArrayList<>();
    static ArrayList<Integer>ans=new ArrayList<>();
    static boolean[]rec;
    static int min=Integer.MAX_VALUE;
    static ArrayList<Task>tasks=new ArrayList<>();
    private static void solve() throws IOException {
        long n=sc.nextLong();
        long []prime=new long[1000001];
        prime[1]=1;
        for (int i=2;i<=n;++i){
            if (prime[i]!=0) continue;
            for (int j=2*i;j<=n;j+=i)prime[j]=i;
        }
        //for (int i=1;i<=20;++i) System.out.print(prime[i]+" ");
        long maxP=prime[(int )n],ans=Long.MAX_VALUE;
        for (long i=n-maxP+1;i<=n;++i) if (i-prime[(int)i]+1<ans) ans=i-prime[(int)i]+1;
        pr.println(ans);
    }
    public static class Task{
        double val;
        int ind;
        public Task(double   w,int v) {
            this.val = w;
            this.ind=v;
        }
    }
    public static void printSolve(StringBuilder str, int[] colors, int n,int color){
        for(int i = 1;i<=n;++i)
            if(colors[i] == color)
                str.append(i + " ");
        str.append('\n');
    }
    public static class pairTask{
        int  val;
        int size;
        public pairTask(int   x, int  y) {
            this.val = x;
            this.size = y;
        }
    }
    public static void subTree(int src,int parent){
        countSubTree[src]=1;
        for (int v:list[src]){
            if (v==parent)
                continue;
            subTree(v,src);
            countSubTree[src]+=countSubTree[v];
        }
    }
    public static boolean prime(long src){
        for (int i=2;i*i<=src;i++){
            if (src%i==0)
                return false;
        }
        return true;
    }
    public static void bfsColor(int src){
        Queue<Integer>queue = new ArrayDeque<>();
        queue.add(src);
        while (!queue.isEmpty()){
            boolean b=false;
            int vertex=-1,p=-1;
            int poll=queue.remove();
            for (int v:list[poll]){
                if (color [v]==0){
                    vertex=v;
                    break;
                }
            }
            for (int v:list[poll]){
                if (color [v]!=0&&v!=vertex){
                    p=v;
                    break;
                }
            }
            for (int v:list[p]){
                if (color [v]!=0){
                    color[vertex]=color[v];
                    b=true;
                    break;
                }
            }
            if (!b){
                color[vertex]=color[poll]+1;
            }
        }
    }
    static int add(int a,int b ){
        if (a+b>=div)
            return (int)(a+b-div);
        return (int)a+b;
    }
    public static int isBipartite(ArrayList<Integer>[]list,int src){
        color[src]=0;
        Queue<Integer>queue=new LinkedList<>();
        int []ans={0,0};
        queue.add(src);
        while (!queue.isEmpty()){
            ans[color[src=queue.poll()]]++;
            for (int v:list[src]){
                if (color[v]==-1){
                    queue.add(v);
                    color[v]=color[src]^1;
                }else if (color[v]==color[src])
                    check=false;
            }
        }
        return add(pow[ans[0]],pow[ans[1]]);
    }
    public static int powerMod(long b, long e){
        long ans=1;
        while (e-->0){
            ans=ans*b%div;
        }
        return (int)ans;
    }
    public static int dfs(int s){
        int ans=1;
        visited[s]=true;
        for (int k:list[s]){
            if (!visited[k]){
                ans+=dfs(k);
            }
        }
        return ans;
    }
    public static int[] radixSort(int[] f) {
        int[] to = new int[f.length];
        {
            int[] b = new int[65537];
            for (int i = 0; i < f.length; i++) b[1 + (f[i] & 0xffff)]++;
            for (int i = 1; i <= 65536; i++) b[i] += b[i - 1];
            for (int i = 0; i < f.length; i++) to[b[f[i] & 0xffff]++] = f[i];
            int[] d = f;
            f = to;
            to = d;
        }
        {
            int[] b = new int[65537];
            for (int i = 0; i < f.length; i++) b[1 + (f[i] >>> 16)]++;
            for (int i = 1; i <= 65536; i++) b[i] += b[i - 1];
            for (int i = 0; i < f.length; i++) to[b[f[i] >>> 16]++] = f[i];
            int[] d = f;
            f = to;
            to = d;
        }
        return f;
    }
    public static long []primeFactor(int n){
        long []prime=new long[n+1];
        prime[1]=1;
        for (int i=2;i<=n;i++)
            prime[i]=((i&1)==0)?2:i;
        for (int i=3;i*i<=n;i++){
            if (prime[i]==i){
                for (int j=i*i;j<=n;j+=i){
                    if (prime[j]==j)
                        prime[j]=i;
                }
            }
        }
        return prime;
    }
    public static StringBuilder binaryradix(long number){
        StringBuilder builder=new StringBuilder();
        long remainder;
        while (number!=0) {
            remainder = number % 2;
            number >>= 1;
            builder.append(remainder);
        }
        builder.reverse();
        return builder;
    }
    public static int binarySearch(long[] a, int index,long target) {
            int l = index;
            int h = a.length - 1;
            while (l<=h) {
                int med = l + (h-l)/2;
                if(a[med] - target <= target) {
                    l = med + 1;
                }
                else h = med  - 1;
            }
            return h;
    }
    public static int val(char c){
        return c-'0';
    }
    public static long gcd(long a,long b) {
        if (a == 0) return b;
        return gcd(b % a, a);
    }
        private static class Pair implements Comparable<Pair> {
            long x;
            long y;

            Pair() {
                this.x = 0;
                this.y = 0;
            }

            Pair(long x, long y) {
                this.x = x;
                this.y = y;
            }

            @Override
            public boolean equals(Object obj) {
                if (this == obj) {
                    return true;
                }
                if (obj == null) return false;
                Pair other = (Pair) obj;
                if (this.x == other.x && this.y == other.y) {
                    return true;
                }
                return false;
            }

            @Override
            public int compareTo(Pair other) {
                if (this.x != other.x) return Long.compare(this.x, other.x);
                return Long.compare(this.y*other.x, this.x*other.y);
            }
    }

    public static void main(String[] args) throws IOException {
        sc = new Scanner(System.in);
        pr = new Printer(System.out);
        solve();

        pr.close();
       // sc.close();
    }
    private static class Scanner {
        BufferedReader br;

        Scanner (InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
        }

        private boolean isPrintable(int ch) {
            return ch >= '!' && ch <= '~';
        }

        private boolean isCRLF(int ch) {
            return ch == '\n' || ch == '\r' || ch == -1;
        }

        private int nextPrintable() {
            try {
                int ch;
                while (!isPrintable(ch = br.read())) {
                    if (ch == -1) {
                        throw new NoSuchElementException();
                    }
                }

                return ch;
            } catch (IOException e) {
                throw new NoSuchElementException();
            }
        }

        String next() {
            try {
                int ch = nextPrintable();
                StringBuilder sb = new StringBuilder();
                do {
                    sb.appendCodePoint(ch);
                } while (isPrintable(ch = br.read()));

                return sb.toString();
            } catch (IOException e) {
                throw new NoSuchElementException();
            }
        }

        int nextInt() {
            try {
                // parseInt from Integer.parseInt()
                boolean negative = false;
                int res = 0;
                int limit = -Integer.MAX_VALUE;
                int radix = 10;

                int fc = nextPrintable();
                if (fc < '0') {
                    if (fc == '-') {
                        negative = true;
                        limit = Integer.MIN_VALUE;
                    } else if (fc != '+') {
                        throw new NumberFormatException();
                    }
                    fc = br.read();
                }
                int multmin = limit / radix;

                int ch = fc;
                do {
                    int digit = ch - '0';
                    if (digit < 0 || digit >= radix) {
                        throw new NumberFormatException();
                    }
                    if (res < multmin) {
                        throw new NumberFormatException();
                    }
                    res *= radix;
                    if (res < limit + digit) {
                        throw new NumberFormatException();
                    }
                    res -= digit;

                } while (isPrintable(ch = br.read()));

                return negative ? res : -res;
            } catch (IOException e) {
                throw new NoSuchElementException();
            }
        }

        long nextLong() {
            try {
                // parseLong from Long.parseLong()
                boolean negative = false;
                long res = 0;
                long limit = -Long.MAX_VALUE;
                int radix = 10;

                int fc = nextPrintable();
                if (fc < '0') {
                    if (fc == '-') {
                        negative = true;
                        limit = Long.MIN_VALUE;
                    } else if (fc != '+') {
                        throw new NumberFormatException();
                    }
                    fc = br.read();
                }
                long multmin = limit / radix;

                int ch = fc;
                do {
                    int digit = ch - '0';
                    if (digit < 0 || digit >= radix) {
                        throw new NumberFormatException();
                    }
                    if (res < multmin) {
                        throw new NumberFormatException();
                    }
                    res *= radix;
                    if (res < limit + digit) {
                        throw new NumberFormatException();
                    }
                    res -= digit;

                } while (isPrintable(ch = br.read()));

                return negative ? res : -res;
            } catch (IOException e) {
                throw new NoSuchElementException();
            }
        }

        float nextFloat() {
            return Float.parseFloat(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        String nextLine() {
            try {
                int ch;
                while (isCRLF(ch = br.read())) {
                    if (ch == -1) {
                        throw new NoSuchElementException();
                    }
                }
                StringBuilder sb = new StringBuilder();
                do {
                    sb.appendCodePoint(ch);
                } while (!isCRLF(ch = br.read()));

                return sb.toString();
            } catch (IOException e) {
                throw new NoSuchElementException();
            }
        }

        void close() {
            try {
                br.close();
            } catch (IOException e) {
//				throw new NoSuchElementException();
            }
        }
    }
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }

    static class List {
        String Word;
        int length;

        List(String Word, int length) {
            this.Word = Word;
            this.length = length;
        }
    }
    private static class Printer extends PrintWriter {
        Printer(PrintStream out) {
            super(out);
        }
    }
}