Problem C. DP (Optimized)

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

#define pb push_back
#define int long long
#define uint __int128
#define mp make_pair
#define left left_compile
#define right right_compile

#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")

const int INF = (int)1e15;
const int md = (int)998244353;
const int MAXN = (int)1e18;
const int N = (int)2e5 + 111;
//const int L = 20;
const int debug = 0;
const long double eps = 1e-7;

mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count());

struct DSU{
    int n;
    vector<int> parent;
    vector<int> sz;
    vector<int> deep;
    DSU(int nn){
        n = nn;
        parent.resize(n+1);
        sz.resize(n+1,1);
        deep.resize(n+1,1);
        for(int i = 0; i <= n; i++)
            parent[i] = i, sz[i] = 1, deep[i] = 1;
    }
    int find_parent(int x){
        if(parent[x] == x)
            return x;
        return parent[x] = find_parent(parent[x]);
    }
    void union_sets(int a,int b){
        a = find_parent(a);
        b = find_parent(b);
        if(a == b)
            return;
        if(deep[a] <= deep[b])
            parent[a] = b, sz[b] += sz[a], deep[b] = max(deep[b],deep[a]+1);
        else
            parent[b] = a, sz[a] += sz[b], deep[a] = max(deep[a],deep[b]+1);
    }
    bool connected(int a,int b){
        return find_parent(a) == find_parent(b);
    }
};

//typedef tree<
//int,
//null_type,
//less_equal<int>,
//rb_tree_tag,
//tree_order_statistics_node_update>
//ordered_set;

int bpow(int a,int b){
    if(b <= 0)
        return 1ll;
    if(b % 2 == 0){
        int t = bpow(a,b/2) % md;
        return (t * t) % md;
    }
    return (a * bpow(a,b-1)) % md;
}

int inv(int a){ /// return 1/a by PRIME modulo md
    return bpow(a,md-2);
}

//void myerase(ordered_set& st, int t){
//    int r = st.order_of_key(t);
//    ordered_set::iterator it = st.find_by_order(r);
//    st.erase(it);
//    return;
//}

void init(){
    return;
}

void add(int& a,int b){
    a = (a + b >= md ? a + b - md : a + b);
}

//void sub(int& a,int b){
//    a = (a < b ? a - b + md : a - b);
//}

__int128 dp[1001];

void solve(){
    int n;
    cin >> n;

    dp[0] = 1;
    for(int i = 1; i <= n; i += 2){
        for(int j = 0; j <= n; j++){
            if(j + i <= n)
                dp[j+i] += dp[j];
        }
    }

    string ans = "";
    while(dp[n] > 0){
        ans = (char)(dp[n] % 10 + '0') + ans;
        dp[n] /= 10;
    }

    cout << ans;

    return;
}
/// abcdefghijklmnopqrstuvwxyz
/// x * sqrt(2) <= d
/// k * x * sqrt(2) <= d
/// x <= d / (sqrt(2) * k)

signed main(){
    ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
//    freopen("input.txt","r",stdin);
//    freopen("product.out","w",stdout);

    init();

    int tests = 1;
//    cin >> tests;

    for(int _ = 1; _ <= tests; _++){
        solve();
    }

//    #ifdef __WIN32
//        cerr << endl << "finished in " << clock() * 1.0 / CLOCKS_PER_SEC << " sec" << endl;
//    #endif

    return 0;
}
/***

bbabbabababbaaa

9
+ passwords
+ paroli
? 1
? 2
- 1
? 2
+ parol
? 2
? 3


***/