CodeForces 387C George and Number

题目链接：http://codeforces.com/problemset/problem/387/C

George and Number

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

George is a cat, so he really likes to play. Most of all he likes to play with his array of positive integers b. During the game, George modifies the array by using special changes. Let's mark George's current array as b₁, b₂, ..., b_|b| (record |b| denotes the current length of the array). Then one change is a sequence of actions:

• Choose two distinct indexes i and j (1 ≤ i, j ≤ |b|; i ≠ j), such that b_i ≥ b_j.
• Get number v = concat(b_i, b_j), where concat(x, y) is a number obtained by adding number y to the end of the decimal record of number x. For example, concat(500, 10) = 50010, concat(2, 2) = 22.
• Add number v to the end of the array. The length of the array will increase by one.
• Remove from the array numbers with indexes i and j. The length of the array will decrease by two, and elements of the array will become re-numbered from 1 to current length of the array.

George played for a long time with his array b and received from array b an array consisting of exactly one number p. Now George wants to know: what is the maximum number of elements array b could contain originally? Help him find this number. Note that originally the array could contain only positive integers.

Input

The first line of the input contains a single integer p (1 ≤ p < 10¹⁰⁰⁰⁰⁰). It is guaranteed that number p doesn't contain any leading zeroes.

Output

Print an integer — the maximum number of elements array b could contain originally.

Examples

Input

9555

Output

4

Input

10000000005

Output

2

Input

800101

Output

3

Input

45

Output

1

Input

1000000000000001223300003342220044555

Output

17

Input

19992000

Output

1

Input

310200

Output

2

Note

Let's consider the test examples:

• Originally array b can be equal to {5, 9, 5, 5}. The sequence of George's changes could have been: {5, 9, 5, 5} → {5, 5, 95} → {95, 55} → {9555}.
• Originally array b could be equal to {1000000000, 5}. Please note that the array b cannot contain zeros.
• Originally array b could be equal to {800, 10, 1}.
• Originally array b could be equal to {45}. It cannot be equal to {4, 5}, because George can get only array {54} from this array in one operation.

Note that the numbers can be very large.

题意：有一个游戏规则是这样的：给定一个正整数数组，从数组中选取两个数，将大的放在前面，小的放在后面，然后拼接在一起组成一个数，取代

这两个数放在数组中。如果用同一个数组玩很多次时，最后得到仅仅只有一个数组。问：给你最后那一个数，那么它的原来数组最大元素数目为多大？

给出的数p满足1<=p<10100000.注意的是，原数组只含有正整数。

解法：这是一道贪心。贪心策略是怎样？既然要使得最后元素个数最大，那么我们可以从后面开始将串分成两个部分的子串，该子串满足：

                                                       1.前面的串表示的数大于等于该串表示的数；

                                                       2.该串表示的数要尽量小。找到之后计数一次，接着将前面的串当成新的串继续找，直至不能够找到为止。

                                                          这样求出的解一定是最优的。

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cmath>
#include<algorithm>
using namespace std;
string str;
bool compare(int L1,int R1,int L2, int R2)
{
    int len1=R1-L1+1,len2=R2-L2+1;
    if(len1>len2) return true;
    else if(len1<len2) return false;
    else{
        int i;
        for(i=0;i<len1;i++){
            if(str[i+L1]>str[i+L2]) return true;
            else if(str[i+L1]<str[i+L2]) return false;
        }
        if(i==len1) return true;
    }
}
int main()
{
    while(cin>>str){
       int y=str.size()-2,r=str.size()-1,ans=1;
       while(y>=0)
       {
          while(y>=0 && str[y+1]=='0') y--;
          if(compare(0,y,y+1,r))
          {
             ans++;
             r=y;
             y--;
          }
          else break;
       }
       cout << ans << endl;
    }
    return 0;
}