/**
* Solution by Charles Ran (polarity.sh)
* Date: 2025-05-06
* Contest: COCI 2016
* Problem: zoltan
**/
#include <bits/stdc++.h>
using namespace std;
using ull = unsigned long long;
using ll = long long;
using vi = vector<int>;
using vl = vector<ll>;
using pii = pair<int, int>;
#define pb push_back
#define rep(i, a, b) for(int i = (a); i < (b); ++i)
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()
const int MAX_N = 1e5 + 1;
const ll MOD = 1e9 + 7;
/**
* DATASTRUCTURE: Segment Tree
* PURPOSE: Range Updates and Queries
* TIME: O(log n) to update and query
*/
template <class T> class SegmentTree {
private:
const T UNIT = {0, 0};
T combine(T a, T b){
if (a.first == b.first){
return {a.first, (a.second + b.second) % MOD};
}
return max(a, b);
}
vector<T> segtree;
int len;
public:
SegmentTree(int len) : len(len), segtree(len * 2, UNIT) {}
void set(int ind, T val) {
ind += len;
segtree[ind] = val;
for (; ind > 1; ind /= 2) {
segtree[ind / 2] = combine(segtree[ind], segtree[ind ^ 1]);
}
}
// [start, end)
T query(int start, int end) {
T ans = UNIT;
for (start += len, end += len; start < end; start /= 2, end /= 2) {
if (start % 2 == 1) { ans = combine(ans, segtree[start++]); }
if (end % 2 == 1) { ans = combine(ans, segtree[--end]); }
}
return ans;
}
};
/**
* ALGORITHM: Modular Exponentiation
* PURPOSE: Computes x^n (mod m)
* CONSTRAINT: m * m <= LLONG_MAX to prevent overflow
* TIME: O(log n)
*/
ll mod_exp(ll x, ll n, ll m) {
x %= m;
ll res = 1;
while (n > 0) {
if (n % 2 == 1) { res = res * x % m; }
x = x * x % m;
n /= 2;
}
return res;
}
/** TOOL: Debug
* PURPOSE: Prints various data types to terminal
* SOURCE: tourist
*/
template <typename A, typename B>
string to_string(pair<A, B> p);
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);
string to_string(const string& s) {
return '"' + s + '"';
}
string to_string(const char* s) {
return to_string((string) s);
}
string to_string(bool b) {
return (b ? "true" : "false");
}
string to_string(vector<bool> v) {
bool first = true;
string res = "{";
for (int i = 0; i < static_cast<int>(v.size()); i++) {
if (!first) {
res += ", ";
}
first = false;
res += to_string(v[i]);
}
res += "}";
return res;
}
template <size_t N>
string to_string(bitset<N> v) {
string res = "";
for (size_t i = 0; i < N; i++) {
res += static_cast<char>('0' + v[i]);
}
return res;
}
template <typename A>
string to_string(A v) {
bool first = true;
string res = "{";
for (const auto &x : v) {
if (!first) {
res += ", ";
}
first = false;
res += to_string(x);
}
res += "}";
return res;
}
template <typename A, typename B>
string to_string(pair<A, B> p) {
return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ")";
}
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
cerr << " " << to_string(H);
debug_out(T...);
}
void solve(){
int n; cin >> n;
vi a(n);
rep(i, 0, n){
cin >> a[i];
}
sort(all(a));
int cnt = 1;
map<int, int> b;
rep(i, 0, n){
if (i != 0 && a[i] != a[i - 1]){
cnt++;
}
b[a[i]] = cnt;
}
rep(i, 0, n){
a[i] = b[a[i]];
}
vi ra = a;
reverse(all(ra));
vector<pii> arr(n + 2, {0, 0});
arr[n + 1] = {0, 1};
SegmentTree<pii> st(n + 2), nst(n + 2);
st.set(n + 1, {0, 1});
rep(i, 0, n){
int x = ra[i];
pii amt = st.query(x + 1, n + 2);
amt.first++;
if (arr[x].first == amt.first){
arr[x].second += amt.second;
arr[x].second %= MOD;
} else {
arr[x] = amt;
}
st.set(x, arr[x]);
if (i == n - 2){
rep(j, 0, n + 2){
nst.set(j, arr[j]);
}
}
}
pii nlis = nst.query(0, n + 1);
pii lis = st.query(0, n + 1);
int mx = lis.first;
auto mult = [&](pii lis, pii nlis, int rem) -> ll {
if (nlis.first == lis.first || lis.first == 0){
ll ans = (ll) nlis.second * mod_exp(2, rem - lis.first - 1, MOD) % MOD;
ans += (ll) (lis.second + MOD - nlis.second) * mod_exp(2, rem - lis.first, MOD) % MOD;
return ans % MOD;
}
return (ll) lis.second * mod_exp(2, rem - lis.first, MOD) % MOD;
};
ll num = mult(lis, nlis, n);
vector<pii> arr2(n + 1, {0, 0});
arr2[0] = {0, 1};
SegmentTree<pii> st2(n + 1);
st2.set(0, {0, 1});
rep(i, 0, n - 1){
int j = n - 1 - i;
int x = ra[i];
pii amt = st2.query(0, x);
amt.first++;
pii li = st.query(x + 1, n + 2);
pii nli = nst.query(x + 1, n + 2);
// debug_out(amt);
// debug_out(nli);
// debug_out(li);
if (li.first + amt.first > mx){
mx = li.first + amt.first;
num = (mult(li, nli, n - amt.first) * (ll) amt.second) % MOD;
} else if (li.first + amt.first == mx){
num += (mult(li, nli, n - amt.first) * (ll) amt.second) % MOD;
num %= MOD;
}
if (arr2[x].first == amt.first){
arr2[x].second += amt.second;
arr2[x].second %= MOD;
} else {
arr2[x] = amt;
}
st2.set(x, arr2[x]);
}
cout << mx << " " << num << endl;
}
int main(){
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
solve();
return 0;
}
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