#include <algorithm>
#include <array>
#include <cassert>
#include <cmath>
#include <iostream>
#include <queue>
#include <vector>
using namespace std;

template<typename T> ostream& operator<<(ostream &os, const vector<T> &v) { os << '{'; string sep; for (const auto &x : v) os << sep << x, sep = ", "; return os << '}'; }
template<typename T, size_t size> ostream& operator<<(ostream &os, const array<T, size> &arr) { os << '{'; string sep; for (const auto &x : arr) os << sep << x, sep = ", "; return os << '}'; }
template<typename A, typename B> ostream& operator<<(ostream &os, const pair<A, B> &p) { return os << '(' << p.first << ", " << p.second << ')'; }

void dbg_out() { cerr << endl; }
template<typename Head, typename... Tail> void dbg_out(Head H, Tail... T) { cerr << ' ' << H; dbg_out(T...); }

#ifdef NEAL_DEBUG
#define dbg(...) cerr << "(" << #__VA_ARGS__ << "):", dbg_out(__VA_ARGS__)
#else
#define dbg(...)
#endif

// This is noticeably faster than std::complex for some reason.
template<typename float_t>
struct complex {
    float_t x, y;

    complex<float_t>(float_t _x = 0, float_t _y = 0) : x(_x), y(_y) {}

    float_t real() const { return x; }
    float_t imag() const { return y; }

    void real(float_t _x) { x = _x; }
    void imag(float_t _y) { y = _y; }

    complex<float_t>& operator+=(const complex<float_t> &other) { x += other.x; y += other.y; return *this; }
    complex<float_t>& operator-=(const complex<float_t> &other) { x -= other.x; y -= other.y; return *this; }

    complex<float_t> operator+(const complex<float_t> &other) const { return complex<float_t>(*this) += other; }
    complex<float_t> operator-(const complex<float_t> &other) const { return complex<float_t>(*this) -= other; }

    complex<float_t> operator*(const complex<float_t> &other) const {
        return {x * other.x - y * other.y, x * other.y + other.x * y};
    }

    complex<float_t> operator*(float_t mult) const {
        return {x * mult, y * mult};
    }

    friend complex<float_t> conj(const complex<float_t> &c) {
        return {c.x, -c.y};
    }

    friend ostream& operator<<(ostream &os, const complex<float_t> &c) {
        return os << '(' << c.x << ", " << c.y << ')';
    }
};

template<typename float_t>
complex<float_t> polar(float_t magnitude, float_t angle) {
    return {magnitude * cos(angle), magnitude * sin(angle)};
}

namespace FFT {
    using float_t = double;

    const float_t ONE = 1;
    const float_t PI = acos(-ONE);

    vector<complex<float_t>> roots = {{0, 0}, {1, 0}};
    vector<int> bit_reverse;

    bool is_power_of_two(int n) {
        return (n & (n - 1)) == 0;
    }

    int round_up_power_two(int n) {
        while (n & (n - 1))
            n = (n | (n - 1)) + 1;

        return max(n, 1);
    }

    // Given n (a power of two), finds k such that n == 1 << k.
    int get_length(int n) {
        assert(is_power_of_two(n));
        return __builtin_ctz(n);
    }

    // Rearranges the indices to be sorted by lowest bit first, then second lowest, etc., rather than highest bit first.
    // This makes even-odd div-conquer much easier.
    void bit_reorder(int n, vector<complex<float_t>> &values) {
        if (int(bit_reverse.size()) != n) {
            bit_reverse.assign(n, 0);
            int length = get_length(n);

            for (int i = 1; i < n; i++)
                bit_reverse[i] = (bit_reverse[i >> 1] >> 1) | ((i & 1) << (length - 1));
        }

        for (int i = 0; i < n; i++)
            if (i < bit_reverse[i])
                swap(values[i], values[bit_reverse[i]]);
    }

    void prepare_roots(int n) {
        if (int(roots.size()) >= n)
            return;

        int length = get_length(int(roots.size()));
        roots.resize(n);

        // The roots array is set up such that for a given power of two n >= 2, roots[n / 2] through roots[n - 1] are
        // the first half of the n-th roots of unity.
        while (1 << length < n) {
            float_t min_angle = 2 * PI / (1 << (length + 1));

            for (int i = 0; i < 1 << (length - 1); i++) {
                int index = (1 << (length - 1)) + i;
                roots[2 * index] = roots[index];
                roots[2 * index + 1] = polar(ONE, min_angle * (2 * i + 1));
            }

            length++;
        }
    }

    void fft_iterative(int n, vector<complex<float_t>> &values) {
        assert(is_power_of_two(n));
        prepare_roots(n);
        bit_reorder(n, values);

        for (int len = 1; len < n; len *= 2)
            for (int start = 0; start < n; start += 2 * len)
                for (int i = 0; i < len; i++) {
                    const complex<float_t> &even = values[start + i];
                    complex<float_t> odd = values[start + len + i] * roots[len + i];
                    values[start + len + i] = even - odd;
                    values[start + i] = even + odd;
                }
    }

    inline complex<float_t> extract(int n, const vector<complex<float_t>> &values, int index, int side) {
        if (side == -1) {
            // Return the product of 0 and 1.
            int other = (n - index) & (n - 1);
            return (conj(values[other] * values[other]) - values[index] * values[index]) * complex<float_t>(0, 0.25);
        }

        int other = (n - index) & (n - 1);
        int sign = side == 0 ? +1 : -1;
        complex<float_t> multiplier = side == 0 ? complex<float_t>(0.5, 0) : complex<float_t>(0, -0.5);
        return multiplier * complex<float_t>(values[index].real() + values[other].real() * sign,
                                             values[index].imag() - values[other].imag() * sign);
    }

    void invert_fft(int n, vector<complex<float_t>> &values) {
        assert(n >= 2);

        for (int i = 0; i < n; i++)
            values[i] = conj(values[i]) * (ONE / n);

        for (int i = 0; i < n / 2; i++) {
            complex<float_t> first = values[i] + values[n / 2 + i];
            complex<float_t> second = (values[i] - values[n / 2 + i]) * roots[n / 2 + i];
            values[i] = first + second * complex<float_t>(0, 1);
        }

        fft_iterative(n / 2, values);

        for (int i = n - 1; i >= 0; i--)
            values[i] = i % 2 == 0 ? values[i / 2].real() : values[i / 2].imag();
    }

    const int FFT_CUTOFF = 150;
    const double SPLIT_CUTOFF = 2e15;
    const int SPLIT_BASE = 1 << 15;

    template<typename T_out, typename T_in>
    vector<T_out> square(const vector<T_in> &input) {
        if (input.empty())
            return {};

        int n = int(input.size());

#ifdef NEAL
        // Sanity check to make sure I'm not forgetting to split.
        double max_value = *max_element(input.begin(), input.end());
        assert(n * max_value * max_value < SPLIT_CUTOFF);
#endif

        // Brute force when n is small enough.
        if (n < 1.5 * FFT_CUTOFF) {
            vector<T_out> result(2 * n - 1);

            for (int i = 0; i < n; i++) {
                result[2 * i] += T_out(input[i]) * input[i];

                for (int j = i + 1; j < n; j++)
                    result[i + j] += T_out(2) * input[i] * input[j];
            }

            return result;
        }

        int N = round_up_power_two(n);
        assert(N >= 2);
        prepare_roots(2 * N);
        vector<complex<float_t>> values(N, 0);

        for (int i = 0; i < n; i += 2)
            values[i / 2] = complex<float_t>(input[i], i + 1 < n ? input[i + 1] : 0);

        fft_iterative(N, values);

        for (int i = 0; i <= N / 2; i++) {
            int j = (N - i) & (N - 1);
            complex<float_t> even = extract(N, values, i, 0);
            complex<float_t> odd = extract(N, values, i, 1);
            complex<float_t> aux = even * even + odd * odd * roots[N + i] * roots[N + i];
            complex<float_t> tmp = even * odd;
            values[i] = aux - complex<float_t>(0, 2) * tmp;
            values[j] = conj(aux) - complex<float_t>(0, 2) * conj(tmp);
        }

        for (int i = 0; i < N; i++)
            values[i] = conj(values[i]) * (ONE / N);

        fft_iterative(N, values);
        vector<T_out> result(2 * n - 1);

        for (int i = 0; i < int(result.size()); i++) {
            float_t value = i % 2 == 0 ? values[i / 2].real() : values[i / 2].imag();
            result[i] = T_out(is_integral<T_out>::value ? round(value) : value);
        }

        return result;
    }

    // Note: `circular = true` can be used for a 2x speedup when only the `max(n, m) - min(n, m) + 1` fully overlapping
    // ranges are needed. It computes results using indices modulo the power-of-two FFT size; see the brute force below.
    template<typename T_out, typename T_in>
    vector<T_out> multiply(const vector<T_in> &left, const vector<T_in> &right, bool circular = false) {
        if (left.empty() || right.empty())
            return {};

        if (left == right && !circular)
            return square<T_out>(left);

        int n = int(left.size());
        int m = int(right.size());

#ifdef NEAL
        // Sanity check to make sure I'm not forgetting to split.
        double max_left = *max_element(left.begin(), left.end());
        double max_right = *max_element(right.begin(), right.end());
        assert(max(n, m) * max_left * max_right < SPLIT_CUTOFF);
#endif

        int output_size = circular ? round_up_power_two(max(n, m)) : n + m - 1;

        // Brute force when either n or m is small enough.
        if (min(n, m) < FFT_CUTOFF) {
            auto &&mod_output_size = [&](int x) {
                return x < output_size ? x : x - output_size;
            };

            vector<T_out> result(output_size, 0);

            for (int i = 0; i < n; i++)
                for (int j = 0; j < m; j++)
                    result[mod_output_size(i + j)] += T_out(left[i]) * right[j];

            return result;
        }

        int N = round_up_power_two(output_size);
        vector<complex<float_t>> values(N, 0);

        for (int i = 0; i < n; i++)
            values[i].real(left[i]);

        for (int i = 0; i < m; i++)
            values[i].imag(right[i]);

        fft_iterative(N, values);

        for (int i = 0; i <= N / 2; i++) {
            int j = (N - i) & (N - 1);
            complex<float_t> product_i = extract(N, values, i, -1);
            values[i] = product_i;
            values[j] = conj(product_i);
        }

        invert_fft(N, values);
        vector<T_out> result(output_size, 0);

        for (int i = 0; i < output_size; i++)
            result[i] = T_out(is_integral<T_out>::value ? round(values[i].real()) : values[i].real());

        return result;
    }

    // Note: `circular = true` can be used for a 2x speedup when only the `max(n, m) - min(n, m) + 1` fully overlapping
    // ranges are needed. It computes results using indices modulo the power-of-two FFT size; see the brute force below.
    vector<int> mod_multiply(const vector<int> &left, const vector<int> &right, int mod, bool split, bool circular = false) {
        if (left.empty() || right.empty())
            return {};

        int n = int(left.size());
        int m = int(right.size());

        for (int i = 0; i < n; i++)
            assert(0 <= left[i] && left[i] < mod);

        for (int i = 0; i < m; i++)
            assert(0 <= right[i] && right[i] < mod);

#ifdef NEAL
        // Sanity check to make sure I'm not forgetting to split.
        assert(split || (double) max(n, m) * mod * mod < SPLIT_CUTOFF);
#endif

        int output_size = circular ? round_up_power_two(max(n, m)) : n + m - 1;

        // Brute force when either n or m is small enough. Brute force up to higher values when split = true.
        if (min(n, m) < (split ? 2 : 1) * FFT_CUTOFF) {
            auto &&mod_output_size = [&](int x) {
                return x < output_size ? x : x - output_size;
            };

            const uint64_t U64_BOUND = numeric_limits<uint64_t>::max() - uint64_t(mod) * mod;
            vector<uint64_t> result(output_size, 0);

            for (int i = 0; i < n; i++)
                for (int j = 0; j < m; j++) {
                    int index = mod_output_size(i + j);
                    result[index] += uint64_t(left[i]) * right[j];

                    if (result[index] > U64_BOUND)
                        result[index] %= mod;
                }

            for (uint64_t &x : result)
                if (x >= uint64_t(mod))
                    x %= mod;

            return vector<int>(result.begin(), result.end());
        }

        if (!split) {
            const vector<uint64_t> &product = multiply<uint64_t>(left, right, circular);
            vector<int> result(output_size, 0);

            for (int i = 0; i < output_size; i++)
                result[i] = int(product[i] % mod);

            return result;
        }

        int N = round_up_power_two(output_size);
        vector<complex<float_t>> left_fft(N, 0), right_fft(N, 0);

        for (int i = 0; i < n; i++) {
            left_fft[i].real(left[i] % SPLIT_BASE);
            left_fft[i].imag(left[i] / SPLIT_BASE);
        }

        fft_iterative(N, left_fft);

        if (left == right) {
            copy(left_fft.begin(), left_fft.end(), right_fft.begin());
        } else {
            for (int i = 0; i < m; i++) {
                right_fft[i].real(right[i] % SPLIT_BASE);
                right_fft[i].imag(right[i] / SPLIT_BASE);
            }

            fft_iterative(N, right_fft);
        }

        vector<complex<float_t>> product(N);
        vector<int> result(output_size, 0);

        for (int exponent = 0; exponent <= 2; exponent++) {
            uint64_t multiplier = 1;

            for (int k = 0; k < exponent; k++)
                multiplier = multiplier * SPLIT_BASE % mod;

            fill(product.begin(), product.end(), 0);

            for (int x = 0; x < 2; x++)
                for (int y = 0; y < 2; y++)
                    if (x + y == exponent)
                        for (int i = 0; i < N; i++)
                            product[i] += extract(N, left_fft, i, x) * extract(N, right_fft, i, y);

            invert_fft(N, product);

            for (int i = 0; i < output_size; i++) {
                uint64_t value = uint64_t(round(product[i].real()));
                result[i] = int((result[i] + value % mod * multiplier) % mod);
            }
        }

        return result;
    }

    vector<int> mod_power(const vector<int> &v, int exponent, int mod, bool split) {
        assert(exponent >= 0);
        vector<int> result = {1};

        if (exponent == 0)
            return result;

        for (int k = 31 - __builtin_clz(exponent); k >= 0; k--) {
            result = mod_multiply(result, result, mod, split);

            if (exponent >> k & 1)
                result = mod_multiply(result, v, mod, split);
        }

        return result;
    }

    // Multiplies many polynomials whose total degree is n in O(n log^2 n).
    vector<int> mod_multiply_all(const vector<vector<int>> &polynomials, int mod, bool split) {
        if (polynomials.empty())
            return {1};

        struct compare_size {
            bool operator()(const vector<int> &x, const vector<int> &y) {
                return x.size() > y.size();
            }
        };

        priority_queue<vector<int>, vector<vector<int>>, compare_size> pq(polynomials.begin(), polynomials.end());

        while (pq.size() > 1) {
            vector<int> a = pq.top(); pq.pop();
            vector<int> b = pq.top(); pq.pop();
            pq.push(mod_multiply(a, b, mod, split));
        }

        return pq.top();
    }
}

template<const int &MOD>
struct _m_int {
    int val;

    _m_int(int64_t v = 0) {
        if (v < 0) v = v % MOD + MOD;
        if (v >= MOD) v %= MOD;
        val = int(v);
    }

    static int inv_mod(int a, int m = MOD) {
        // https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm#Example
        int g = m, r = a, x = 0, y = 1;

        while (r != 0) {
            int q = g / r;
            g %= r; swap(g, r);
            x -= q * y; swap(x, y);
        }

        return x < 0 ? x + m : x;
    }

    explicit operator int() const { return val; }
    explicit operator int64_t() const { return val; }

    _m_int& operator+=(const _m_int &other) {
        val -= MOD - other.val;
        if (val < 0) val += MOD;
        return *this;
    }

    _m_int& operator-=(const _m_int &other) {
        val -= other.val;
        if (val < 0) val += MOD;
        return *this;
    }

    static unsigned fast_mod(uint64_t x, unsigned m = MOD) {
#if !defined(_WIN32) || defined(_WIN64)
        return unsigned(x % m);
#endif
        // Optimized mod for Codeforces 32-bit machines.
        // x must be less than 2^32 * m for this to work, so that x / m fits in a 32-bit unsigned int.
        unsigned x_high = unsigned(x >> 32), x_low = unsigned(x);
        unsigned quot, rem;
        asm("divl %4\n"
            : "=a" (quot), "=d" (rem)
            : "d" (x_high), "a" (x_low), "r" (m));
        return rem;
    }

    _m_int& operator*=(const _m_int &other) {
        val = fast_mod(uint64_t(val) * other.val);
        return *this;
    }

    _m_int& operator/=(const _m_int &other) {
        return *this *= other.inv();
    }

    friend _m_int operator+(const _m_int &a, const _m_int &b) { return _m_int(a) += b; }
    friend _m_int operator-(const _m_int &a, const _m_int &b) { return _m_int(a) -= b; }
    friend _m_int operator*(const _m_int &a, const _m_int &b) { return _m_int(a) *= b; }
    friend _m_int operator/(const _m_int &a, const _m_int &b) { return _m_int(a) /= b; }

    _m_int& operator++() {
        val = val == MOD - 1 ? 0 : val + 1;
        return *this;
    }

    _m_int& operator--() {
        val = val == 0 ? MOD - 1 : val - 1;
        return *this;
    }

    _m_int operator++(int) { _m_int before = *this; ++*this; return before; }
    _m_int operator--(int) { _m_int before = *this; --*this; return before; }

    _m_int operator-() const {
        return val == 0 ? 0 : MOD - val;
    }

    bool operator==(const _m_int &other) const { return val == other.val; }
    bool operator!=(const _m_int &other) const { return val != other.val; }

    _m_int inv() const {
        return inv_mod(val);
    }

    _m_int pow(int64_t p) const {
        if (p < 0)
            return inv().pow(-p);

        _m_int a = *this, result = 1;

        while (p > 0) {
            if (p & 1)
                result *= a;

            p >>= 1;

            if (p > 0)
                a *= a;
        }

        return result;
    }

    friend ostream& operator<<(ostream &os, const _m_int &m) {
        return os << m.val;
    }
};

extern const int MOD = 1e9 + 7;
using mod_int = _m_int<MOD>;

struct union_find {
    // When data[x] < 0, x is a root and -data[x] is its tree size. When data[x] >= 0, data[x] is x's parent.
    vector<int> data;
    int components = 0;

    union_find(int n = -1) {
        if (n >= 0)
            init(n);
    }

    void init(int n) {
        data.assign(n + 1, -1);
        components = n;
    }

    int find(int x) {
        return data[x] < 0 ? x : data[x] = find(data[x]);
    }

    int get_size(int x) {
        return -data[find(x)];
    }

    bool unite(int x, int y) {
        x = find(x);
        y = find(y);

        if (x == y)
            return false;

        if (-data[x] < -data[y])
            swap(x, y);

        data[x] += data[y];
        data[y] = x;
        components--;
        return true;
    }
};


int main() {
    ios::sync_with_stdio(false);
#ifndef NEAL_DEBUG
    cin.tie(nullptr);
#endif

    int N;
    cin >> N;
    vector<int> P(N);
    union_find UF(N);

    for (int &p : P) {
        cin >> p;

        if (p >= 0)
            p--;
    }

    for (int i = 0; i < N; i++)
        if (P[i] >= 0)
            UF.unite(i, P[i]);

    vector<int> regular, special;
    vector<bool> done(N, false);

    for (int i = 0; i < N; i++)
        if (P[i] < 0) {
            int root = UF.find(i);
            special.push_back(UF.get_size(root));
            done[root] = true;
        }

    for (int i = 0; i < N; i++)
        if (!done[i] && UF.find(i) == i)
            regular.push_back(UF.get_size(i));

    int R = int(regular.size());
    int S = int(special.size());
    int special_sum = 0;

    for (int s : special)
        special_sum += s;

    mod_int answer = mod_int(N) * mod_int(N - 1).pow(S);
    mod_int component_total = (R + S) * mod_int(N - 1).pow(S);

    for (int s : special)
        component_total -= (N - s) * mod_int(N - 1).pow(S - 1);

    vector<vector<int>> polynomials;

    for (int i = 0; i < S; i++)
        polynomials.push_back({1, special[i]});

    vector<int> result = FFT::mod_multiply_all(polynomials, MOD, true);
    mod_int cycle_total = 0, factorial = 1;

    for (int c = 2; c <= S; c++) {
        cycle_total += result[c] * factorial * mod_int(N - 1).pow(S - c);
        factorial *= c;
    }

    component_total += cycle_total;
    answer -= component_total;
    cout << answer << '\n';
}


Measured memory_bytes: 4788