Training 1 - B题

In the city of Saint Petersburg, a day lasts for 2100 minutes. From the main station of Saint Petersburg, a train departs after 1 minute, 4 minutes, 16 minutes, and so on; in other words, the train departs at time 4k for each integer k≥0. Team BowWow has arrived at the station at the time ss and it is trying to count how many trains have they missed; in other words, the number of trains that have departed strictly before time ss. For example if s=20, then they missed trains which have departed at 1, 4 and 16. As you are the only one who knows the time, help them!
Note that the number ss will be given you in a binary representation without leading zeroes.

Input

The first line contains a single binary number s (0≤s<2100) without leading zeroes.

Output

Output a single number — the number of trains which have departed strictly before the time ss.

Examples

Input

100000000

Output

4

Input

101

Output

2

Input

10100

Output

3

Note

In the first example 1000000002=256101000000002=25610, missed trains have departed at 11, 44, 1616 and 6464.
In the second example 1012=5101012=510, trains have departed at 11 and 44.
The third example is explained in the statements.

#pragma warning (disable:4996)
#include <iostream>
#include <algorithm>
#include <iomanip>
#include <cstring>
#include <string>
#include <cstdio>
#include <cmath>
#include <vector>
#include <queue>
#include <set>
#define inf 0X3f3f3f3f
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
const int maxn = 1e6 + 5;

string str;

int main()
{
	int ans = 0;
	cin >> str;
	bool flag = 1;
	for (int i = 1; i < str.length(); i++)
		if (str[i] == '1')
		{
			flag = 0;
			break;
		}
	if (str.length() % 2 == 0)
		ans = str.length() / 2;
	else
	{
		ans = (str.length() - 1) / 2 + 1;
		if (flag)
			ans--;
	}
	printf("%d\n", ans);
}

思路：
二进制数能表示的最大的4进制数就是它最高位是1其他位是0时的数。特别地，如果二进制数本身是4的次幂，不包括这个数本身。