Problem:
Score : 1300 points

Problem Statement

We will call a non-negative integer increasing if, for any two adjacent digits in its decimal representation, the digit to the right is greater than or equal to the digit to the left.
For example, 1558, 11, 3 and 0 are all increasing; 10 and 20170312 are not.

Snuke has an integer N. Find the minimum number of increasing integers that can represent N as their sum.

Constraints

1 \leq N \leq 10^{500000}

Input

The input is given from Standard Input in the following format:

N

Output

Print the minimum number of increasing integers that can represent N as their sum.

Sample Input 1

80

Sample Output 1

2

One possible representation is 80 = 77 + 3.

Sample Input 2

123456789

Sample Output 2

1

123456789 in itself is increasing, and thus it can be represented as the sum of one increasing integer.

Sample Input 3

20170312

Sample Output 3

4

Sample Input 4

7204647845201772120166980358816078279571541735614841625060678056933503

Sample Output 4

31

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

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 Main {
	static InputStream is;
	static PrintWriter out;
	static String INPUT = "";
	
	static void solve()
	{
		char[] s = ns().toCharArray();
		int n = s.length;
		int[] o = new int[n];
		for(int i = 0;i < n;i++)o[i] = s[i]-'0';
		int low = 0, high = 500003*10/9;
		while(high - low > 1){
			int h = high+low>>1;
			if(ok(h, Arrays.copyOf(o, n))){
				high = h;
			}else{
				low = h;
			}
		}
		out.println(high);
	}
	
	static boolean ok(int h, int[] s)
	{
		int lim = h*9;
		int n = s.length;
		int nz = 0;
		for(int i = n-1;i >= 0;i--){
			int u = 0;
			if(nz <= i-8){
				u = 99999999;
			}
			if(u == 0){
				for(int j = Math.max(0, i-7);j <= i;j++){
					u = u * 10 + s[j];
				}
			}
			lim = Math.min(u, lim);
			if(lim < s[i])return false;
			lim = (lim-s[i])/10*10;
			s[i] -= lim;
			for(int j = i;j >= 0 && s[j] < 0;j--){
				int q = (-s[j]+9)/10;
				s[j] += q*10;
				s[j-1] -= q;
			}
			while(nz < i && s[nz] == 0)nz++;
		}
		return true;
	}
	
	public static void main(String[] args) throws Exception
	{
//		int n = 500000, m = 99999;
//		Random gen = new Random();
//		StringBuilder sb = new StringBuilder();
//		for (int i = 0; i < n; i++) {
//			sb.append(gen.nextInt(10));
//		}
//		INPUT = sb.toString();

		
		long S = System.currentTimeMillis();
		is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		solve();
		out.flush();
		long G = System.currentTimeMillis();
		tr(G-S+"ms");
	}
	
	private static boolean eof()
	{
		if(lenbuf == -1)return true;
		int lptr = ptrbuf;
		while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;
		
		try {
			is.mark(1000);
			while(true){
				int b = is.read();
				if(b == -1){
					is.reset();
					return true;
				}else if(!isSpaceChar(b)){
					is.reset();
					return false;
				}
			}
		} catch (IOException e) {
			return true;
		}
	}
	
	private static byte[] inbuf = new byte[1024];
	static int lenbuf = 0, ptrbuf = 0;
	
	private static 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 static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
//	private static boolean isSpaceChar(int c) { return !(c >= 32 && c <= 126); }
	private static int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private static double nd() { return Double.parseDouble(ns()); }
	private static char nc() { return (char)skip(); }
	
	private static String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private static 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 static 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 static int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private static 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 static 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 static void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }
}