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:
import java.io.*;
import java.util.*;

public class G {

	static final int P = 1_000_000_007;

	int[][] ways;
	int[][] pow;

	void preCalc(int sz) {
		ways = new int[sz][];
		for (int i = 0; i < ways.length; i++) {
			ways[i] = new int[i + 1];
			ways[i][0] = ways[i][i] = 1;
			for (int j = 1; j < i; j++) {
				ways[i][j] = (ways[i - 1][j] + ways[i - 1][j - 1]) % P;
			}
		}

		pow = new int[10][sz];
		pow[0] = null;
		for (int i = 1; i <= 9; i++) {
			pow[i][0] = 1;
			for (int j = 1; j < sz; j++) {
				pow[i][j] = (int) ((long) pow[i][j - 1] * i % P);
			}
		}
	}

	int solve(String ss) {
		int n = ss.length();
		int[] s = new int[n];
		for (int i = 0; i < n; i++) {
			s[i] = ss.charAt(i) - '0';
		}

		preCalc(n + 10);

		int[] ans = new int[n + 1];

		int[] cnt = new int[10];

		for (int i = 0; i < n; i++) {

			int rest = n - i - 1;

			int dig = s[i];

			for (int j = 0; j <= (i == n - 1 ? dig : dig - 1); j++) {
				cnt[j]++; // now we have one more digit >= j

				for (int use = 1; use < 10; use++) {
					// use digits are bad, 10 - use are good
					for (int cntGood = 0; cntGood <= rest; cntGood++) {
						int delta = (int) ((long) ways[rest][cntGood]
								* pow[use][rest - cntGood] % P
								* pow[10 - use][cntGood] % P);
						int idx = cnt[use] + cntGood;
						ans[idx] += delta;
						if (ans[idx] >= P) {
							ans[idx] -= P;
						}
					}
				}

				// System.err.println(Arrays.toString(ans));

			}

			cnt[dig]++;

		}
		
		int ret = 0;
		long mult = 0;
		for (int i = 1; i < ans.length; i++) {
			mult = (10L * mult + 1) % P;
			ret += (int)(mult * ans[i] % P);
			if (ret >= P) {
				ret -= P;
			}
		}
		
		return ret;
	}

	void submit() {
		out.println(solve(nextToken()));
	}

	void stress() {

	}

	void test() {
		StringBuilder sb = new StringBuilder("1");
		for (int i = 0; i < 700; i++) {
			sb.append('0');
		}
		solve(sb.toString());
	}

	G() throws IOException {
		br = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
		submit();
		// stress();
//		 test();
		out.close();
	}

	static final Random rng = new Random();

	static int rand(int l, int r) {
		return l + rng.nextInt(r - l + 1);
	}

	public static void main(String[] args) throws IOException {
		new G();
	}

	BufferedReader br;
	PrintWriter out;
	StringTokenizer st;

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

	String nextString() {
		try {
			return br.readLine();
		} catch (IOException e) {
			throw new RuntimeException(e);
		}
	}

	int nextInt() {
		return Integer.parseInt(nextToken());
	}

	long nextLong() {
		return Long.parseLong(nextToken());
	}

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