One day Mr. Takahashi picked up a dictionary containing all of the N! permutations of integers 1 through N. The dictionary has N! pages, and page i (1 ≤ i ≤ N!) contains the i-th permutation in the lexicographical order.

Mr. Takahashi wanted to look up a certain permutation of length N in this dictionary, but he forgot some part of it.

His memory of the permutation is described by a sequence P_1, P_2, ..., P_N. If P_i = 0, it means that he forgot the i-th element of the permutation; otherwise, it means that he remembered the i-th element of the permutation and it is P_i.

He decided to look up all the possible permutations in the dictionary. Compute the sum of the page numbers of the pages he has to check, modulo 10^9 + 7.

Constraints

* 1 ≤ N ≤ 500000
* 0 ≤ P_i ≤ N
* P_i ≠ P_j if i ≠ j (1 ≤ i, j ≤ N), P_i ≠ 0 and P_j ≠ 0.

Input

The input is given from Standard Input in the following format:


N
P_1 P_2 ... P_N


Output

Print the sum of the page numbers of the pages he has to check, as modulo 10^9 + 7.

Examples

Input

4
0 2 3 0


Output

23


Input

3
0 0 0


Output

21


Input

5
1 2 3 5 4


Output

2


Input

1
0


Output

1


Input

10
0 3 0 0 1 0 4 0 0 0


Output

953330050
/**
 * code generated by JHelper
 * More info: https://github.com/AlexeyDmitriev/JHelper
 * @author RiaD
 */

#include <iostream>
#include <fstream>

#include <iostream>
#include <vector>



#include <cstddef>


#include <type_traits>

template <typename T, typename = std::true_type>
struct IdentityHelper;

template <typename T>
struct IdentityHelper<T, typename std::is_arithmetic<T>::type> {
	static T identity() {
		return 1;
	}
};

template <typename T>
T identity() {
	return IdentityHelper<T>::identity();
}





template <bool b, typename T = void>
using enable_if_t = typename std::enable_if<b, T>::type;



#include <iterator>


#include <string>
#include <stdexcept>

#ifndef SPCPPL_ASSERT
	#ifdef SPCPPL_DEBUG
		#define SPCPPL_ASSERT(condition) \
		if(!(condition)) { \
			throw std::runtime_error(std::string() + #condition + " in line " + std::to_string(__LINE__) + " in " + __PRETTY_FUNCTION__); \
		}
	#else
		#define SPCPPL_ASSERT(condition)
	#endif
#endif


/**
* Support decrementing and multi-passing, but not declared bidirectional(or even forward) because
* it's reference type is not a reference.
*
* It doesn't return reference because
* 1. Anyway it'll not satisfy requirement [forward.iterators]/6
*   If a and b are both dereferenceable, then a == b if and only if *a and
*   b are bound to the same object.
* 2. It'll not work with reverse_iterator that returns operator * of temporary which is temporary for this iterator
*
* Note, reverse_iterator is not guaranteed to work  now too since it works only with bidirectional iterators,
* but it's seems to work at least on my implementation.
*
* It's not really useful anywhere except iterating anyway.
*/
template <typename T>
class IntegerIterator: public std::iterator<std::input_iterator_tag, T, std::ptrdiff_t, T*, T> {
public:
	explicit IntegerIterator(T value): value(value) {

	}

	IntegerIterator& operator++() {
		++value;
		return *this;
	}

	IntegerIterator operator++(int) {
		IntegerIterator copy = *this;
		++value;
		return copy;
	}

	IntegerIterator& operator--() {
		--value;
		return *this;
	}

	IntegerIterator operator--(int) {
		IntegerIterator copy = *this;
		--value;
		return copy;
	}

	T operator*() const {
		return value;
	}

	bool operator==(IntegerIterator rhs) const {
		return value == rhs.value;
	}

	bool operator!=(IntegerIterator rhs) const {
		return !(*this == rhs);
	}

private:
	T value;
};

template <typename T>
class IntegerRange {
public:
	IntegerRange(T begin, T end): begin_(begin), end_(end) {
		SPCPPL_ASSERT(begin <= end);
	}

	IntegerIterator<T> begin() const {
		return IntegerIterator<T>(begin_);
	}

	IntegerIterator<T> end() const {
		return IntegerIterator<T>(end_);
	}

private:
	T begin_;
	T end_;
};

template <typename T>
class ReversedIntegerRange {
	typedef std::reverse_iterator<IntegerIterator<T>> IteratorType;
public:
	ReversedIntegerRange(T begin, T end): begin_(begin), end_(end) {
		SPCPPL_ASSERT(begin >= end);
	}

	IteratorType begin() const {
		return IteratorType(IntegerIterator<T>(begin_));
	}

	IteratorType end() const {
		return IteratorType(IntegerIterator<T>(end_));
	}

private:
	T begin_;
	T end_;
};

template <typename T>
IntegerRange<T> range(T to) {
	return IntegerRange<T>(0, to);
}

template <typename T>
IntegerRange<T> range(T from, T to) {
	return IntegerRange<T>(from, to);
}

template <typename T>
IntegerRange<T> inclusiveRange(T to) {
	return IntegerRange<T>(0, to + 1);
}

template <typename T>
IntegerRange<T> inclusiveRange(T from, T to) {
	return IntegerRange<T>(from, to + 1);
}

template <typename T>
ReversedIntegerRange<T> downrange(T from) {
	return ReversedIntegerRange<T>(from, 0);
}

template <typename T>
ReversedIntegerRange<T> downrange(T from, T to) {
	return ReversedIntegerRange<T>(from, to);
}

template <typename T>
ReversedIntegerRange<T> inclusiveDownrange(T from) {
	return ReversedIntegerRange<T>(from + 1, 0);
}

template <typename T>
ReversedIntegerRange<T> inclusiveDownrange(T from, T to) {
	return ReversedIntegerRange<T>(from + 1, to);
}


template <typename T>
std::vector<T> factorials(std::size_t maxN) {
	std::vector<T> res(maxN + 1);
	res[0] = identity<T>();
	for (std::size_t i = 1; i <= maxN; ++i) {
		res[i] = res[i - 1] * static_cast<long long>(i);
	}
	return res;
}

template <typename T>
std::vector<std::vector<T>> binomials(std::size_t maxN) {
	std::vector<std::vector<T>> res(maxN + 1, std::vector<T>(maxN + 1));
	for (std::size_t n = 0; n <= maxN; ++n) {
		res[n][0] = identity<T>();
		res[n][n] = identity<T>();
		for (std::size_t k = 1; k < n; ++k) {
			res[n][k] = res[n - 1][k - 1] + res[n - 1][k];
		}
	}

	return res;
}

template <typename T, typename U, typename = enable_if_t<std::is_integral<U>::value>>
T binomial(U n, U k) {
	if (k > n || k < 0) {
		return T();
	}
	T res = identity<T>();
	for (U i: inclusiveRange(1, k)) {
		res *= n - i + 1;
		res /= i;
	}
	return res;
};

template <typename T, typename U, typename = enable_if_t<std::is_integral<U>::value>>
T starsAndBars(U stars, U groups) {
	if (groups == 0) {
		if (stars == 0) {
			return identity<T>();
		} else {
			return T();
		}
	}
	return binomial<T>(stars + groups - 1, groups - 1);
};



#include <functional>









#include <utility>

template <typename T>
constexpr auto hasBegin(int) -> decltype(std::begin(std::declval<T>()), true) {
	return true;
}

template <typename T>
constexpr bool hasBegin(...) {
	return false;
}

template <typename T>
using IsContainer = std::integral_constant<bool, hasBegin<T>(0)>;




template <typename T, typename Merge>
class SegmentTreeBase {
protected:
	SegmentTreeBase(std::size_t n, const T& defaultValue = T(), const Merge& merge = Merge()):
			n(n),
			defaultValue(defaultValue),
			shift(calculateShift(n)),
			values(shift << 1, defaultValue),
			merge(merge) {

	}

	template <typename R, typename = enable_if_t<IsContainer<R>::value>>
	SegmentTreeBase(const R& range, const T& defaultValue = T(), const Merge& merge = Merge()) :
			SegmentTreeBase(
					static_cast<std::size_t>(std::distance(std::begin(range), std::end(range))),
					defaultValue,
					merge
			) {
		std::copy(std::begin(range), std::end(range), values.begin() + shift);
		for (std::size_t index: downrange(shift, static_cast<std::size_t>(1))) {
			recalculate(index);
		}
	}

	static std::size_t calculateShift(std::size_t n) {
		std::size_t result = 1;
		while (result < n) {
			result <<= 1;
		}
		return result;
	}

	void recalculate(std::size_t index) {
		values[index] = merge(values[2 * index], values[2 * index + 1]);
	}

	std::size_t n;
	T defaultValue;
	std::size_t shift;
	std::vector<T> values;
	Merge merge;
};


template <typename T, typename Merge>
class BottomUpSegmentTree: protected SegmentTreeBase<T, Merge> {
public:

	template <typename R>
	BottomUpSegmentTree(const R& range, const T& defaultValue = T(), const Merge& merge = Merge()):
			SegmentTreeBase<T, Merge>(range, defaultValue, merge) {

	}

	const T& getElement(std::size_t index) {
		SPCPPL_ASSERT(index < n);
		return values[index + shift];
	}

	T getResult(std::size_t l, std::size_t r) const {
		SPCPPL_ASSERT(l <= r && r <= n);
		return internalGetResult(l + shift, r + shift);
	}

	template <typename Updater>
	void update(std::size_t index, const Updater& updater) {
		SPCPPL_ASSERT(index < n);
		index += shift;
		updater(values[index]);
		for (std::size_t parent = index / 2; parent > 0; parent /= 2) {
			this->recalculate(parent);
		}
	}

	void set(std::size_t index, const T& value) {
		return update(index, [&value](T& element) {
			element = value;
		});
	}

protected:
	typedef SegmentTreeBase<T, Merge> Base;
	using Base::n;
	using Base::defaultValue;
	using Base::shift;
	using Base::values;
	using Base::merge;

private:
	T internalGetResult(std::size_t l, std::size_t r) const {
		if (l == r) {
			return defaultValue;
		}
		if (l & 1) {
			return merge(values[l], internalGetResult(l + 1, r));
		}
		if (r & 1) {
			return merge(internalGetResult(l, r - 1), values[r - 1]);
		}
		return internalGetResult(l / 2, r / 2);
	}
};


template <typename T>
class BottomUpSumSegmentTree: public BottomUpSegmentTree<T, std::plus<T>> {
public:
	template <typename R>
	BottomUpSumSegmentTree(
			const R& range,
			const T& zero = T()
	): BottomUpSegmentTree<T, std::plus<T>>(range, zero) {
	}

};




#include <assert.h>





/**
* ax + by = result
*/
template <typename T>
T extendedGcd(T a, T b, T& x, T& y) {
	if (a == 0) {
		x = 0;
		y = 1;
		return b;
	}
	T d = extendedGcd(b % a, a, y, x);
	x -= (b / a) * y;
	return d;
}

template <typename T>
class Zn {
public:
	Zn(): value(0) {
	}

	/**
	* Instead of ctor, to allow not to normalize in ctor
	*/
	static Zn valueOf(int value) {
		int x = value % mod();
		if (x < 0) {
			x += mod();
		}
		return Zn(x);
	}

	static Zn valueOf(long long value) {
		int x = static_cast<int>(value % mod());
		if (x < 0) {
			x += mod();
		}
		return Zn(x);
	}

	static Zn rawValueOf(int value) {
		SPCPPL_ASSERT(value >= 0 && value < mod());
		return Zn(value);
	}

	Zn& operator=(int rhs) {
		return *this = Zn::valueOf(rhs);
	}

	Zn& operator=(long long rhs) {
		return *this = Zn::valueOf(rhs);
	}

	Zn& operator+=(const Zn& rhs) {
		value += rhs.value;
		if (value >= mod()) {
			value -= mod();
		}
		return *this;
	}

	Zn& operator+=(int rhs) {
		return *this += Zn::valueOf(rhs);
	}

	Zn& operator+=(long long rhs) {
		return *this += Zn::valueOf(rhs);
	}

	Zn& operator-=(const Zn& rhs) {
		value -= rhs.value;
		if (value < 0) {
			value += mod();
		}
		return *this;
	}

	Zn& operator-=(int rhs) {
		return *this -= Zn::valueOf(rhs);
	}

	Zn& operator-=(long long rhs) {
		return *this -= Zn::valueOf(rhs);
	}

	Zn& operator*=(const Zn& rhs) {
		long long result = static_cast<long long>(value) * static_cast<long long>(rhs.value);
		value = static_cast<int>(result % mod());
		return *this;
	}

	Zn& operator*=(int rhs) {
		return *this *= Zn::valueOf(rhs);
	}

	Zn& operator*=(long long rhs) {
		return *this *= Zn::valueOf(rhs);
	}

	Zn operator-() const {
		if (value == 0) {
			return *this;
		}
		else {
			return Zn(mod() - value);
		}
	}

	Zn& operator/=(const Zn& rhs) {
		return *this *= rhs.inversed();
	}

	Zn& operator/=(int rhs) {
		return *this /= Zn::valueOf(rhs);
	}

	Zn& operator/=(long long rhs) {
		return *this /= Zn::valueOf(rhs);
	}

	bool operator==(const Zn& rhs) const {
		return value == rhs.value;
	}

	Zn inversed() const {
		SPCPPL_ASSERT(value != 0);

		int x, y;
		int gcd = extendedGcd(value, mod(), x, y);
		(void) gcd;
		SPCPPL_ASSERT(gcd == 1);

		if (x < 0) {
			x += mod();
		}
		return Zn(x);
	}

	template <typename U>
	friend std::ostream& operator<<(std::ostream&, const Zn<U>& zn);

	template <typename U>
	friend std::istream& operator>>(std::istream&, Zn<U>& zn);

	int intValue() const {
		return value;
	}

private:
	/**
	* No normalization performed
	*/
	explicit Zn(int value): value(value) {
	}

	int value;

	constexpr static int mod() {
		return T::value;
	}

	template <int N = T::value>
	static constexpr bool positive_or_runtime(int) {
		return N > 0;
	}
	static constexpr bool positive_or_runtime(...) {
		return true;
	}
	static_assert(
			std::is_same<typename std::decay<decltype(T::value)>::type, int>::value,
			"T::value must be int"
	);
	static_assert(positive_or_runtime(0), "Mod has to be positive integer");
};

template <typename T>
bool operator==(const Zn<T>& lhs, int rhs) {
	return lhs == Zn<T>::valueOf(rhs);
}

template <typename T>
bool operator==(int lhs, const Zn<T>& rhs) {
	return rhs == lhs;
}
template <typename T>
bool operator==(const Zn<T>& lhs, long long rhs) {
	return lhs == Zn<T>::valueOf(rhs);
}

template <typename T>
bool operator==(long long lhs, Zn<T>& rhs) {
	return rhs == lhs;
}

template <typename T>
bool operator!=(const Zn<T>& lhs, const Zn<T>& rhs) {
	return !(lhs == rhs);
}

template <typename T>
bool operator!=(const Zn<T>& lhs, int rhs) {
	return !(lhs == rhs);
}

template <typename T>
bool operator!=(int lhs, const Zn<T>& rhs) {
	return !(lhs == rhs);
}

template <typename T>
bool operator!=(const Zn<T>& lhs, long long rhs) {
	return !(lhs == rhs);
}

template <typename T>
bool operator!=(long long rhs, const Zn<T>& lhs) {
	return !(lhs == rhs);
}

template <typename T>
Zn<T> operator+(const Zn<T>& lhs, const Zn<T>& rhs) {
	Zn<T> copy = lhs;
	return copy += rhs;
}

template <typename T>
Zn<T> operator+(const Zn<T>& lhs, int rhs) {
	Zn<T> copy = lhs;
	return copy += rhs;
}

template <typename T>
Zn<T> operator+(int lhs, const Zn<T>& rhs) {
	return rhs + lhs;
}

template <typename T>
Zn<T> operator+(const Zn<T>& lhs, long long rhs) {
	Zn<T> copy = lhs;
	return copy += rhs;
}

template <typename T>
Zn<T> operator+(long long lhs, const Zn<T>& rhs) {
	return rhs + lhs;
}

template <typename T>
Zn<T> operator-(const Zn<T>& lhs, const Zn<T>& rhs) {
	Zn<T> copy = lhs;
	return copy -= rhs;
}

template <typename T>
Zn<T> operator-(const Zn<T>& lhs, int rhs) {
	Zn<T> copy = lhs;
	return copy -= rhs;
}

template <typename T>
Zn<T> operator-(int lhs, const Zn<T>& rhs) {
	return Zn<T>::valueOf(lhs) - rhs;
}

template <typename T>
Zn<T> operator-(const Zn<T>& lhs, long long rhs) {
	Zn<T> copy = lhs;
	return copy -= rhs;
}

template <typename T>
Zn<T> operator-(long lhs, const Zn<T>& rhs) {
	return Zn<T>::valueOf(lhs) - rhs;
}

template <typename T>
Zn<T> operator*(const Zn<T>& lhs, const Zn<T>& rhs) {
	Zn<T> copy = lhs;
	return copy *= rhs;
}

template <typename T>
Zn<T> operator*(const Zn<T>& lhs, int rhs) {
	Zn<T> copy = lhs;
	return copy *= rhs;
}

template <typename T>
Zn<T> operator*(int lhs, const Zn<T>& rhs) {
	return rhs * lhs;
}

template <typename T>
Zn<T> operator*(const Zn<T>& lhs, long long rhs) {
	Zn<T> copy = lhs;
	return copy *= rhs;
}

template <typename T>
Zn<T> operator*(long long lhs, const Zn<T>& rhs) {
	return rhs * lhs;
}

template <typename T>
Zn<T> operator/(const Zn<T>& lhs, const Zn<T>& rhs) {
	Zn<T> copy = lhs;
	return copy /= rhs;
}

template <typename T>
Zn<T> operator/(const Zn<T>& lhs, int rhs) {
	Zn<T> copy = lhs;
	return copy /= rhs;
}

template <typename T>
Zn<T> operator/(int lhs, const Zn<T>& rhs) {
	return Zn<T>::valueOf(lhs) / rhs;
}

template <typename T>
Zn<T> operator/(const Zn<T>& lhs, long long rhs) {
	Zn<T> copy = lhs;
	return copy /= rhs;
}

template <typename T>
Zn<T> operator/(long long lhs, const Zn<T>& rhs) {
	return Zn<T>::valueOf(lhs) / rhs;
}

template <typename T>
std::ostream& operator<<(std::ostream& stream, const Zn<T>& zn) {
	return stream << zn.value;
}

template <typename T>
std::istream& operator>>(std::istream& stream, Zn<T>& zn) {
	long long value;
	stream >> value;
	zn.value = static_cast<int>(value % T::value);
	return stream;
}

template <typename T>
struct IdentityHelper<Zn<T>> {
	static Zn<T> identity() {
		return Zn<T>::valueOf(1);
	}
};

template <int m>
using ZnConst = Zn<std::integral_constant<int, m>>;


using namespace std;

class TaskE {
public:
	void solve(std::istream& in, std::ostream& out) {
		int n;
		in >> n;
		vector<int> v(n);
		vector<int> used(n);
		for (int i: range(n)) {
			in >> v[i];
			--v[i];
			if (v[i] != -1) {
				++used[v[i]];
			}
		}

		vector<int> unused;
		unused.reserve(n);

		int allEmptys = 0;
		for (int i: range(n)) {
			if (!used[i]) {
				unused.push_back(i);
				++allEmptys;
			}
		}

		using Z = ZnConst<1000000007>;
		Z ans;

		vector<Z> fact = factorials<Z>(n);

		BottomUpSumSegmentTree<int> usedNumbers(n);

		int emptys = 0;
		Z sumHren;
		for (int i: downrange(n)) {
			Z curAdd;
			if (v[i] != -1) {
				int numbersLess = usedNumbers.getResult(0, v[i]);
				curAdd += numbersLess;
				int emptyLess = (int) (lower_bound(unused.begin(), unused.end(), v[i]) - unused.begin());
				if (allEmptys) {
					curAdd += Z::valueOf(emptyLess) * emptys / allEmptys;
				}
				sumHren += (allEmptys - emptyLess);
				usedNumbers.set(v[i], 1);
			}
			else {
				curAdd += emptys * Z::rawValueOf(1) / 2;
				curAdd += sumHren / Z::valueOf(allEmptys);
				++emptys;
			}

			//cerr << i << ' ' << curAdd << ' ' << curAdd * fact[n - 1 - i] << endl;

			ans += curAdd * fact[n - 1 - i];
		}

		//cerr << ans << endl;
		out << (ans + 1) * fact[unused.size()];
	}
};


int main() {
	std::ios_base::sync_with_stdio(false);
	TaskE solver;
	std::istream& in(std::cin);
	std::ostream& out(std::cout);
	solver.solve(in, out);
	in.tie(0);
	out << std::fixed;
	out.precision(20);
	return 0;
}
