1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
#include <bits/stdc++.h>

using namespace std;

typedef unsigned uint;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ldbl;
typedef pair<int, int> pii;
typedef pair<uint, uint> puu;
typedef pair<ll, ll> pll;
typedef pair<ull, ull> pull;
typedef pair<double, double> pdd;
typedef vector<int> vi;
typedef vector<uint> vu;
typedef vector<ll> vll;
typedef vector<ull> vull;
typedef vector<pii> vpii;
typedef vector<puu> vpuu;
typedef vector<pll> vpll;
typedef vector<pull> vpull;
typedef vector<string> vstr;
typedef vector<double> vdbl;
typedef vector<ldbl> vldbl;
#define pb push_back
#define ppb pop_back
#define pfr push_front
#define ppfr pop_front
#define emp emplace
#define empb emplace_back
#define be begin
#define rbe rbegin
#define all(x) (x).be(), (x).end()
#define rall(x) (x).rbe(), (x).rend()
#define fir first
#define sec second
#define mkp make_pair
#define brif(cond) if (cond) break
#define ctif(cond) if (cond) continue
#define retif(cond) if (cond) return
void canhazfast() {ios_base::sync_with_stdio(false);cin.tie(nullptr);cout.tie(nullptr);}
template<typename T> T gcd(T a, T b) {return b ? gcd(b, a%b) : a;}
template<typename T> T extgcd(T a, T b, T &x, T &y)
{
    T x0 = 1, y0 = 0, x1 = 0, y1 = 1;
    while (b) {
        T q = a/b; a %= b; swap(a, b);
        x0 -= q*x1; swap(x0, x1);
        y0 -= q*y1; swap(y0, y1);
    }
    x = x0; y = y0; return a;
}
int ctz(uint x) {return __builtin_ctz(x);}
int ctzll(ull x) {return __builtin_ctzll(x);}
int clz(uint x) {return __builtin_clz(x);}
int clzll(ull x) {return __builtin_clzll(x);}
int popcnt(uint x) {return __builtin_popcount(x);}
int popcntll(ull x) {return __builtin_popcountll(x);}
int bsr(uint x) {return 31^clz(x);}
int bsrll(ull x) {return 63^clzll(x);}

#define N 48
#define NN 27
#define SZ (1<<NN)

int a[N];
int cmin[N], cnt[N];
int adj_msk[N];
//vi adj[N];
ll dp[N][N];
int inv[SZ];

void init_binom(int n)
{
    fill_n(dp[0], n+1, 1);
    for (int i = 1; i <= n; ++i) {
        dp[i][0] = 1;
        for (int j = 1; j <= n-i; ++j) dp[i][j] = dp[i-1][j]+dp[i][j-1];
    }
}

ll binom(int n, int k) { return dp[k][n-k]; }

int main()
{
    canhazfast();

    int n, sz, invmax, inv0 = 0;

    cin >> n;
    invmax = n*(n-1)/2;
    for (int i = 0; i < n; ++i) cin >> a[i];

    for (int i = 0; i < n; ++i) {
        for (int j = i+1; j < n; ++j) {
            if (a[i] > a[j]) {
                adj_msk[i] |= 1<<j;
                adj_msk[j] |= 1<<i;
                //adj[i].pb(j);
                //adj[j].pb(i);
                ++inv0;
            }
        }
    }

    if (inv0 == 0) {
        //cerr << "0 inv\n";
        init_binom(n);
        for (int k = 1; k <= n; ++k) cout << "0 " << binom(n, k) << '\n';
        return 0;
    }
    if (inv0 == invmax) {
        //cerr << "all inv\n";
        init_binom(n);
        for (int k = 1; k <= n; ++k) cout << k*(k-1)/2 << ' ' << binom(n, k) << '\n';
        return 0;
    }
    if (inv0 == 1) {
        //cerr << "1 inv\n";
        init_binom(n);
        cout << "0 " << n << '\n';
        for (int k = 2; k <= n-2; ++k) cout << "0 " << binom(n-2, k)+2*binom(n-2, k-1) << '\n';
        cout << "0 2\n1 1\n";
        return 0;
    }
    if (inv0 == invmax-1) {
        //cerr << "all but 1 inv\n";
        init_binom(n);
        cout << "0 " << n << "\n0 1\n";
        for (int k = 3; k <= n; ++k) cout << k*(k-1)/2-1 << ' ' << binom(n-2, k-2) << '\n';
        return 0;
    }

    retif(n > NN) cout << "fail\n", 0;//xDEAD;

    fill_n(cmin+1, n, n*(n-1)/2);
    sz = 1<<n;
    for (int i = 1; i < sz; ++i) {
        int last = i-(i&-i);
        int v = ctz(i);
        inv[i] = inv[last]+popcnt(i&adj_msk[v]);
        int k = popcnt(i);
        if (cmin[k] > inv[i]) {
            cmin[k] = inv[i];
            cnt[k] = 1;
        } else if (cmin[k] == inv[i]) {
            ++cnt[k];
        }
    }
    for (int k = 1; k <= n; ++k) cout << cmin[k] << ' ' << cnt[k] << '\n';

    return 0;
}