#include<vector>
#include<iostream>
#include<iomanip>
#include<chrono>
#include <random>
#include <cassert>
#include <queue>
#include <set>
#include <cmath>
#include <map>
#include <algorithm>
using namespace std;
typedef long long LL;
#define PB push_back
#define MP make_pair
#define A first
#define B second
#define SZ(x) int(x.size())
#define FR(i, a, b) for (int i = (a); i < (b); ++i)
#define FOR(i, n) FR(i, 0, n)
const int M = 1000000007;
mt19937_64 rnd(chrono::steady_clock::now().time_since_epoch().count());
#ifdef DEBUG
#define LOG(x) std::cout << x << std::endl
#else
#define LOG(X)
#endif
template <typename T>
T inverse(T a, T m) {
T u = 0, v = 1;
while (a != 0) {
T t = m / a;
m -= t * a; swap(a, m);
u -= t * v; swap(u, v);
}
assert(m == 1);
return u;
}
template <typename T>
class Modular {
public:
using Type = typename decay<decltype(T::value)>::type;
constexpr Modular() : value() {}
template <typename U>
Modular(const U& x) {
value = normalize(x);
}
template <typename U>
static Type normalize(const U& x) {
Type v;
if (-mod() <= x && x < mod()) v = static_cast<Type>(x);
else v = static_cast<Type>(x % mod());
if (v < 0) v += mod();
return v;
}
const Type& operator()() const { return value; }
template <typename U>
explicit operator U() const { return static_cast<U>(value); }
constexpr static Type mod() { return T::value; }
Modular& operator+=(const Modular& other) { if ((value += other.value) >= mod()) value -= mod(); return *this; }
Modular& operator-=(const Modular& other) { if ((value -= other.value) < 0) value += mod(); return *this; }
template <typename U> Modular& operator+=(const U& other) { return *this += Modular(other); }
template <typename U> Modular& operator-=(const U& other) { return *this -= Modular(other); }
Modular& operator++() { return *this += 1; }
Modular& operator--() { return *this -= 1; }
Modular operator++(int) { Modular result(*this); *this += 1; return result; }
Modular operator--(int) { Modular result(*this); *this -= 1; return result; }
Modular operator-() const { return Modular(-value); }
template <typename U = T>
typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type& operator*=(const Modular& rhs) {
#ifdef _WIN32
uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x), d, m;
asm(
"divl %4; \n\t"
: "=a" (d), "=d" (m)
: "d" (xh), "a" (xl), "r" (mod())
);
value = m;
#else
value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
#endif
return *this;
}
template <typename U = T>
typename enable_if<is_same<typename Modular<U>::Type, long long>::value, Modular>::type& operator*=(const Modular& rhs) {
long long q = static_cast<long long>(static_cast<long double>(value) * rhs.value / mod());
value = normalize(value * rhs.value - q * mod());
return *this;
}
template <typename U = T>
typename enable_if<!is_integral<typename Modular<U>::Type>::value, Modular>::type& operator*=(const Modular& rhs) {
value = normalize(value * rhs.value);
return *this;
}
Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); }
friend const Type& abs(const Modular& x) { return x.value; }
template <typename U>
friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs);
template <typename U>
friend bool operator<(const Modular<U>& lhs, const Modular<U>& rhs);
template <typename V, typename U>
friend V& operator>>(V& stream, Modular<U>& number);
private:
Type value;
};
template <typename T> bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value == rhs.value; }
template <typename T, typename U> bool operator==(const Modular<T>& lhs, U rhs) { return lhs == Modular<T>(rhs); }
template <typename T, typename U> bool operator==(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) == rhs; }
template <typename T> bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(const Modular<T>& lhs, U rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(U lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T> bool operator<(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value < rhs.value; }
template <typename T> Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T> Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T> Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T> Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
template<typename T, typename U>
Modular<T> power(const Modular<T>& a, const U& b) {
assert(b >= 0);
Modular<T> x = a, res = 1;
U p = b;
while (p > 0) {
if (p & 1) res *= x;
x *= x;
p >>= 1;
}
return res;
}
template <typename T>
bool IsZero(const Modular<T>& number) {
return number() == 0;
}
template <typename T>
string to_string(const Modular<T>& number) {
return to_string(number());
}
// U == std::ostream? but done this way because of fastoutput
template <typename U, typename T>
U& operator<<(U& stream, const Modular<T>& number) {
return stream << number();
}
// U == std::istream? but done this way because of fastinput
template <typename U, typename T>
U& operator>>(U& stream, Modular<T>& number) {
typename common_type<typename Modular<T>::Type, long long>::type x;
stream >> x;
number.value = Modular<T>::normalize(x);
return stream;
}
/*
using ModType = int;
struct VarMod { static ModType value; };
ModType VarMod::value;
ModType& md = VarMod::value;
using Mint = Modular<VarMod>;
*/
constexpr int md = 1000000007;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;
vector<Mint> fact(1, 1);
vector<Mint> inv_fact(1, 1);
Mint C(int n, int k) {
if (k < 0 || k > n) {
return 0;
}
while ((int) fact.size() < n + 1) {
fact.push_back(fact.back() * (int) fact.size());
inv_fact.push_back(1 / fact.back());
}
return fact[n] * inv_fact[k] * inv_fact[n - k];
}
int n;
struct Node {
int len;
Mint cnt;
};
template<class F>
struct segtree {
int cnt;
vector<F> t;
segtree(int cnt) : cnt(cnt) {
t.assign(2 * cnt, {0, 0});
}
inline F merge(F a, F b) {
if (a.len > b.len) return a;
if (b.len > a.len) return b;
if (a.len == 0) return {0, 0};
return {a.len, a.cnt + b.cnt};
}
void modify(int p, F value) {
p += cnt;
t[p] = merge(t[p], value);
for (p >>= 1; p; p >>= 1) {
t[p] = merge(t[p << 1], t[p << 1 | 1]);
}
}
F query(int l, int r) {
F resl = {0, 0}, resr = {0, 0};
for (l += cnt, r += cnt; l < r; l >>= 1, r >>= 1) {
if (l & 1) resl = merge(resl, t[l++]);
if (r & 1) resr = merge(t[--r], resr);
}
return merge(resl, resr);
}
};
Mint pow(int k) {
Mint ext = 1, base = 2;
FOR(i, 30) {
if ((k >> i) & 1) ext *= base;
base *= base;
}
return ext;
}
void solve() {
cin >> n;
vector<int> a(n);
set<int> st;
FOR(i, n) {
cin >> a[i];
st.insert(a[i]);
}
map<int, int> mp;
int cnt = 1;
for (auto i : st) mp[i] = cnt++;
FOR(i, n) a[i] = mp[a[i]];
int N = SZ(st);
vector<Node> inc(n), dec(n);
segtree<Node> T_inc(N + 2), T_dec(N + 2);
for (int i = n - 1; i >= 0; i--) {
Node best_Inc = T_inc.query(a[i] + 1, N + 2);
if (best_Inc.len == 0) inc[i] = {1, 1};
else inc[i] = {best_Inc.len + 1, best_Inc.cnt};
T_inc.modify(a[i], inc[i]);
Node best_Dec = T_dec.query(0, a[i]);
if (best_Dec.len == 0) dec[i] = {1, 1};
else dec[i] = {best_Dec.len + 1, best_Dec.cnt};
T_dec.modify(a[i], dec[i]);
}
int len = 0;
// FOR(i, n) cout << inc[i].len << ' ' << dec[i].len << '\n';
FOR(i, n) len = max(len, inc[i].len + dec[i].len - 1);
Mint ans = 0;
FOR(i, n) {
if (inc[i].len + dec[i].len == len + 1) ans += (Mint)inc[i].cnt * dec[i].cnt;
}
cout << len << ' ' << ans * pow(n - len) << '\n';
}
int main() {
ios::sync_with_stdio(0);
cin.tie(0);
int numtests = 1;
// cin >> numtests;
while(numtests--) {
solve();
}
}
