#include <bits/stdc++.h>

#include "atcoder/modint.hpp"
using mint = atcoder::modint998244353;

#include "testlib.h"

void solve() {
    std::string S = inf.readToken(format("[01]{%d, %d}", 1, 1'000'000));
    inf.readEoln();
    ensure(S[0] == '1');
    std::reverse(S.begin(), S.end());
    int n = S.size();

    mint three = 3;
    mint c0    = mint(2) / 3;
    mint all_  = c0;
    auto t     = c0;
    mint two   = 1;
    mint ans   = 0;
    for (int i = 0; i < n; i++) {
        if (S[i] == '1') {
            ans += two;
            all_ *= three;
            t *= c0;
        } else {
            ans += two * t;
        }
        three *= three;
        two *= 2;
        c0 *= c0;
    }
    std::cout << (ans * all_).val() << std::endl;
}

int main(int argc, char *argv[]) {
    std::cin.tie(0)->sync_with_stdio(0);
    registerValidation(argc, argv);
    solve();
    inf.readEof();
}