Takahashi has an empty string S and a variable x whose initial value is 0.

Also, we have a string T consisting of `0` and `1`.

Now, Takahashi will do the operation with the following two steps |T| times.

* Insert a `0` or a `1` at any position of S of his choice.
* Then, increment x by the sum of the digits in the odd positions (first, third, fifth, ...) of S. For example, if S is `01101`, the digits in the odd positions are `0`, `1`, `1` from left to right, so x is incremented by 2.



Print the maximum possible final value of x in a sequence of operations such that S equals T in the end.

Constraints

* 1 \leq |T| \leq 2 \times 10^5
* T consists of `0` and `1`.

Input

Input is given from Standard Input in the following format:


T


Output

Print the maximum possible final value of x in a sequence of operations such that S equals T in the end.

Examples

Input

1101


Output

5


Input

0111101101


Output

26
// iostream is too mainstream
#include <cstdio>
// bitch please
#include <iostream>
#include <algorithm>
#include <vector>
#include <set>
#include <map>
#include <queue>
#include <stack>
#include <list>
#include <chrono>
#include <random>
#include <cstdlib>
#include <cmath>
#include <ctime>
#include <cstring>
#include <iomanip>
#define dibs reserve
#define OVER9000 1234567890
#define tisic 47
#define soclose 1e-8
#define patkan 9
#define ff first
#define ss second
#define abs(x) (((x) < 0)?-(x):(x))
using uint = unsigned int;
using cat = long long;
using dbl = long double;
constexpr dbl pi = 3.14159265358979323846;
using namespace std;

#ifdef DONLINE_JUDGE
	// palindromic tree is better than splay tree!
	#define lld I64d
#endif

int main() {
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	cout.tie(0);
	cout << fixed << setprecision(10);
	string S;
	cin >> S;
	cat ans = 0;
	for(int i = 0, cur = 0, last = 0; i < (int)S.length(); i++) {
		if(S[i] == '1') {
			ans += i/2+1;
			if(last) cur++, last--;
			else last++;
		}
		else {
			if(last == 1) cur++, last = 0;
			ans += cur;
		}
	}
	cout << ans << "\n";
	return 0;
}

// look at my code
// my code is amazing
