This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#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;
template<typename T> using Tree = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long int ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
#define fastio ios_base::sync_with_stdio(false); cin.tie(NULL)
#define pb push_back
#define endl '\n'
#define sz(a) (int)a.size()
#define setbits(x) __builtin_popcountll(x)
#define ff first
#define ss second
#define conts continue
#define ceil2(x,y) ((x+y-1)/(y))
#define all(a) a.begin(), a.end()
#define rall(a) a.rbegin(), a.rend()
#define yes cout << "Yes" << endl
#define no cout << "No" << endl
#define rep(i,n) for(int i = 0; i < n; ++i)
#define rep1(i,n) for(int i = 1; i <= n; ++i)
#define rev(i,s,e) for(int i = s; i >= e; --i)
#define trav(i,a) for(auto &i : a)
template<typename T>
void amin(T &a, T b) {
    a = min(a,b);
}
template<typename T>
void amax(T &a, T b) {
    a = max(a,b);
}
#ifdef LOCAL
#include "debug.h"
#else
#define debug(x) 42
#endif
/*
refs:
https://youtu.be/RwrBLp8AvJA?t=17698
edi
*/
const int MOD = 1e9 + 7;
const int N = 5e3 + 5;
const int inf1 = int(1e9) + 5;
const ll inf2 = ll(1e18) + 5;
#include "prison.h"
vector<int> dp(N,inf1), best(N);
int ptr = 1;
vector<vector<int>> ans;
int n;
void go(int l, int r, int p, int bag){
    if(l > r) return;
    ans[p][0] = bag;
    rep1(j,l){
        ans[p][j] = -(bag+1);
    }
    for(int j = r; j <= n; ++j){
        ans[p][j] = -((bag^1)+1);
    }
    int len = r-l+1;
    if(len <= 2){
        return;
    }
    int segs = best[len];
    int len1 = (len-2)/segs;
    int len2 = ceil2(len-2,segs);
    int cnt1 = (len-2)/len1;
    int cnt2 = (len-2)%len1;    
    cnt1 -= cnt2;
    assert(cnt1+cnt2 == segs);
    int curr = l+1;
    rep1(i,cnt1){
        for(int j = curr; j <= curr+len1-1; ++j){
            ans[p][j] = ptr;
        }
        go(curr,curr+len1-1,ptr++,bag^1);
        curr += len1;
    }
    rep1(i,cnt2){
        for(int j = curr; j <= curr+len2-1; ++j){
            ans[p][j] = ptr;
        }
        go(curr,curr+len2-1,ptr++,bag^1);
        curr += len2;
    }
}
vector<vector<int>> devise_strategy(int n_) {
    n = n_;
    dp[0] = dp[1] = dp[2] = 0;
    for(int i = 3; i <= n; ++i){
        rep1(j,min(i-2,20)){
            int val = j+dp[ceil2(i-2,j)];
            if(val < dp[i]){
                best[i] = j;
                dp[i] = val;
            }
        }
    }
    ans = vector<vector<int>>(n+1,vector<int>(n+1));
    go(1,n,0,0);
    return ans;
}
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