Language: C++

#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,avx512f")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include <iostream>
#include <iomanip>
#include <string>
#include <cmath>
#include <algorithm>
#include <vector>
#include <set>
#include <map>
#include <unordered_map>
#include <unordered_set>
#include <list>
#include <stack>
#include <queue>
#include <bitset>
#include <numeric>
#include <cassert>
#include <memory>
#include <random>
#include <functional>
#include <complex>
#include <immintrin.h>
#ifdef DEBUG
#include "./Lib/debug_VC.hpp"
#include "./Lib/Timer.hpp"
#include "./Lib/sample.hpp"
#else
#define dump(...)
#endif

/* macro */
#define FOR(i, b, e) for(ll i = (ll)(b); i < (ll)(e); ++i)
#define RFOR(i, b, e) for(ll i = (ll)(e-1); i >= (ll)(b); --i)
#define REP(i, n) FOR(i, 0, n)
#define RREP(i, n) RFOR(i, 0, n)
#define REPC(x,c) for(const auto& x:(c))
#define REPI2(it,b,e) for(auto it = (b); it != (e); ++it)
#define REPI(it,c) REPI2(it, (c).begin(), (c).end())
#define RREPI(it,c) REPI2(it, (c).rbegin(), (c).rend())
#define REPI_ERACE2(it, b, e) for(auto it = (b); it != (e);)
#define REPI_ERACE(it, c) REPI_ERACE2(it, (c).begin(), (c).end())
#define ALL(x) (x).begin(),(x).end()
#define cauto const auto&
/* macro func */
template<class T>
inline auto sort(T& t) { std::sort(ALL(t)); }
template<class T>
inline auto rsort(T& t) { std::sort((t).rbegin(), (t).rend()); }
template<class T>
inline auto unique(T& t) { (t).erase(unique((t).begin(), (t).end()), (t).end()); }
template<class T, class S>
inline auto chmax(T& t, const S& s) { if (s > t) { t = s; return true; } return false; }
template<class T, class S>
inline auto chmin(T& t, const S& s) { if (s < t) { t = s; return true; } return false; }
inline auto BR() { std::cout << "\n"; }

/* type define */
using ll = long long;
using PAIR = std::pair<ll, ll>;
using VS = std::vector<std::string>;
using VL = std::vector<long long>;
using VVL = std::vector<VL>;
using VVVL = std::vector<VVL>;
using VD = std::vector<double>;
template<class T>
using V = std::vector<T>;

/* using std */
using std::cout;
constexpr char endl = '\n';
using std::cin;
using std::pair;
using std::string;
using std::stack;
using std::queue;
using std::vector;
using std::list;
using std::map;
using std::unordered_map;
using std::multimap;
using std::unordered_multimap;
using std::set;
using std::unordered_set;
using std::unordered_multiset;
using std::multiset;
using std::bitset;
using std::priority_queue;

/* Initial processing  */
struct Preprocessing { Preprocessing() { std::cin.tie(0); std::ios::sync_with_stdio(0); }; }_Preprocessing;

/* Remove the source of the bug */
signed pow(signed, signed) { assert(false); return -1; }

/* define hash */
namespace std {
template <>	class hash<std::pair<ll, ll>> { public:	size_t operator()(const std::pair<ll, ll>& x) const { return hash<ll>()(1000000000 * x.first + x.second); } };
}

/* input */
template<class T> std::istream& operator >> (std::istream& is, vector<T>& vec) { for (T& x : vec) is >> x; return is; }

/* constant value */
//constexpr ll MOD = 1000000007;
constexpr ll MOD = 998244353;

//=============================================================================================

class ModCalculator {
	const long long m_mod;
	const std::vector<long long> m_fac;
	const std::vector<long long> m_finv;

	auto constructFac(long long s) {
		std::vector<long long> fac(s);
		fac[0] = fac[1] = 1;
		for (long long i = 2; i < s; ++i) {
			fac[i] = fac[i - 1] * i;
			if (fac[i] > m_mod) { fac[i] %= m_mod; }
		}
		return fac;
	}
	auto constructInv(long long s) {
		std::vector<long long> finv(s);
		finv[s - 1] = this->pow(m_fac[s - 1], m_mod - 2);
		for (long long i = s - 2; i >= 0; --i) {
			finv[i] = finv[i + 1] * (i + 1);
			if (finv[i] > m_mod) { finv[i] %= m_mod; }
		}
		return finv;
	}
public:
	ModCalculator(long long mod = MOD, long long size = 3 * 1e6) :
		m_mod(mod), m_fac(constructFac(size)), m_finv(constructInv(size)) {}

	long long pow(long long a, long long b) const {
		long long ans = 1;
		while (b > 0) {
			if (b & 1) { ans *= a; if (ans > m_mod) { ans %= m_mod; } }
			b >>= 1; a *= a; if (a > m_mod) { a %= m_mod; }
		}
		return ans;
	}

	auto C(int n, int r) const {
		long long val = m_fac[n] * m_finv[r];
		if (val > m_mod) { val %= m_mod; }
		val *= m_finv[n - r];;
		if (val > m_mod) { val %= m_mod; }
		return val;
	}
}calc;

using bit = bitset<101>;

struct TYPE {
	bit b;
	ll size;
	TYPE(const bit& b_, ll size_) :b(b_), size(size_) {}

	bool operator<(const TYPE& r)const {
		if (size == r.size) {
			auto mn = std::min(size, r.size);
			REP(i, mn) {
				if (b[i] == r.b[i]) { continue; }
				return b[i] < r.b[i];
			}
			return size < r.size;
		}
		return size < r.size;
	}
};


auto solve(const bit& b, ll n, bool debug = false) ->ll {
	static map<TYPE, ll> memo;
	if (debug) {
		for (auto&& [p, val] : memo) {
			REP(i, p.size) { cout << p.b[i]; }cout << ": ";
			cout << val << endl;
		}
		return 0LL;
	}
	if (n == 0) { return 1LL; }
	if (n == 1) { return (b[0] == 1) ? 2LL : 1LL; }
	auto key = TYPE{b, n};
	if (memo.find(key) != memo.end()) { return memo[key]; }

	VL dp1(n);// ........0 .......1
	VL dp2(n);// ....(pxl)


	dp1[0] = (b[0] == 1) ? 1 : 0;
	FOR(i, 1, n) {
		dp1[i] = ((b[i] == 1) ? 2 : 1) * solve(b, i);
		if (dp1[i] >= MOD) { dp1[i] -= MOD; }

		/**
		cout << " ---- ";//
		REP(j, i + 1) { cout << b[j]; }BR();///*//**/
		FOR(s, 1, i + 1) {
			auto now = (b >> (i - s + 1));
			/**cout << "now: "; REP(j, s) { cout << now[j]; }BR(); BR();/*//**/
			ll mx = (i + 1) / s + 1;
			FOR(k, 2, mx) {
				now &= (b >> (i - s * k + 1));
				dp2[i] += solve(now, s) * solve(b, i-s*k+1);
				if (dp2[i] >= MOD) { dp2[i] %= MOD; }
				/**dump(s, k);
				cout << "bit: "; REP(j, s) { cout << now[j]; }
				BR(); BR();/*//**/
			}
		}
	}
	/**REP(i, n) { cout << b[i]; }cout << " -> " << dp1[n - 1] << " " << dp2[n - 1] << endl;/*//**/
	ll ans = dp1[n - 1] + dp2[n - 1];
	if (ans >= MOD) { ans %= MOD; }
	memo.emplace(TYPE(b, n), ans);
	return ans;
};

signed main() {
	string s;
	cin >> s;

	const ll n = s.size();
	bit b;
	REP(i, n)if (s[i] == '1') { b[i] = 1; }

	auto ans = solve(b, n);
	cout << ans << endl;

	//solve(b, n, true);
}

Compiler output:
In file included from /usr/include/c++/14/string:43,
                 from /usr/include/c++/14/bits/locale_classes.h:40,
                 from /usr/include/c++/14/bits/ios_base.h:41,
                 from /usr/include/c++/14/ios:44,
                 from /usr/include/c++/14/ostream:40,
                 from /usr/include/c++/14/iostream:41,
                 from a.cc:4:
/usr/include/c++/14/bits/allocator.h: In destructor 'std::__cxx11::basic_string<char>::_Alloc_hider::~_Alloc_hider()':
/usr/include/c++/14/bits/allocator.h:182:7: error: inlining failed in call to 'always_inline' 'std::allocator< <template-parameter-1-1> >::~allocator() noexcept [with _Tp = char]': target specific option mismatch
  182 |       ~allocator() _GLIBCXX_NOTHROW { }
      |       ^
In file included from /usr/include/c++/14/string:54:
/usr/include/c++/14/bits/basic_string.h:186:14: note: called from here
  186 |       struct _Alloc_hider : allocator_type // TODO check __is_final
      |              ^~~~~~~~~~~~