Problem: Let S(n) denote the number that represents the digits of n in sorted order. For example, S(1) = 1, S(5) = 5, S(50394) = 3459, S(353535) = 333555.

Given a number X, compute <image> modulo 109 + 7.

Input

The first line of input will contain the integer X (1 ≤ X ≤ 10700).

Output

Print a single integer, the answer to the question.

Examples

Input

21


Output

195


Input

345342


Output

390548434

Note

The first few values of S are 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 11, 12, 13, 14, 15, 16, 17, 18, 19, 2, 12. The sum of these values is 195. 

Solution (in JAVA):

Solution:
//package goodbye2017;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class G {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		char[] s = ns().toCharArray();
		int mod = 1000000007;
		int m = 702;
		
		long[] bases = new long[m+1];
		bases[0] = 1;
		for(int i = 1;i <= m;i++)bases[i] = bases[i-1] * 10 % mod;
		
		// 10*700^3*10
		long ans = 0;
		for(int d = 9;d >= 1;d--){
			int n = s.length;
			long[] sum = new long[m]; // base
			long[] num = new long[m]; // base
			long esum = 0;
			int ebase = 0;
			for(int i = 0;i < n;i++){
				long[] nsum = new long[m]; // base
				long[] nnum = new long[m]; // base
				for(int j = 0;j < m;j++){
					for(int k = 0;k <= 9;k++){
						if(k > d && j+1 < m){
							nsum[j+1] += sum[j] * 10;
							nsum[j+1] %= mod;
							nnum[j+1] += num[j];
							if(nnum[j+1] >= mod)nnum[j+1] -= mod;
						}
						if(k == d){
							nsum[j] += sum[j] * 10 + num[j] * bases[j];
							nsum[j] %= mod;
							nnum[j] += num[j];
							if(nnum[j] >= mod)nnum[j] -= mod;
						}
						if(k < d){
							nsum[j] += sum[j];
							if(nsum[j] >= mod)nsum[j] -= mod;
							nnum[j] += num[j];
							if(nnum[j] >= mod)nnum[j] -= mod;
						}
					}
				}
				
				for(int k = 0;k < s[i]-'0';k++){
					if(k > d){
						nsum[ebase+1] += esum * 10;
						nsum[ebase+1] %= mod;
						nnum[ebase+1] += 1;
						if(nnum[ebase+1] >= mod)nnum[ebase+1] -= mod;
					}
					if(k == d){
						nsum[ebase] += esum * 10 + bases[ebase];
						nsum[ebase] %= mod;
						nnum[ebase] += 1;
						if(nnum[ebase] >= mod)nnum[ebase] -= mod;
					}
					if(k < d){
						nsum[ebase] += esum;
						if(nsum[ebase] >= mod)nsum[ebase] -= mod;
						nnum[ebase] += 1;
						if(nnum[ebase] >= mod)nnum[ebase] -= mod;
					}
				}
				
				if(s[i]-'0' > d){
					esum = esum * 10;
					esum %= mod;
					ebase++;
				}else if(s[i]-'0' == d){
					esum = esum * 10 + bases[ebase];
					esum %= mod;
				}
				
				sum = nsum;
				num = nnum;
			}
			long all = esum;
			for(int j = 0;j < m;j++){
				all += sum[j];
			}
			ans += all % mod * d;
		}
		out.println(ans%mod);
	}
	
	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new G().run(); }
	
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}