#include using namespace std; #define ms(s, n) memset(s, n, sizeof(s)) #define FOR(i, a, b) for (int i = (a); i < (b); i++) #define FORd(i, a, b) for (int i = (a) - 1; i >= (b); i--) #define FORall(it, a) for (__typeof((a).begin()) it = (a).begin(); it != (a).end(); it++) #define FORalld(it, a) for (__typeof((a).rbegin()) it = (a).rbegin(); it != (a).rend(); it++) #define sz(a) int((a).size()) #define present(t, x) (t.find(x) != t.end()) #define all(a) (a).begin(), (a).end() #define uni(a) (a).erase(unique(all(a)), (a).end()) #define pb push_back #define pf push_front #define mp make_pair #define fi first #define se second #define prec(n) fixed<> (i)) & 1) #define bitcount(n) __builtin_popcountll(n) typedef long long ll; typedef unsigned long long ull; typedef long double ld; typedef pair pi; typedef vector vi; typedef vector vii; const int MOD = (int) 1e9 + 7; const int INF = (int) 1e9; const ll LINF = (ll) 1e18; const ld PI = acos((ld) -1); const ld EPS = 1e-9; inline ll gcd(ll a, ll b) {ll r; while (b) {r = a % b; a = b; b = r;} return a;} inline ll lcm(ll a, ll b) {return a / gcd(a, b) * b;} inline ll fpow(ll n, ll k, int p = MOD) {ll r = 1; for (; k; k >>= 1) {if (k & 1) r = r * n % p; n = n * n % p;} return r;} template inline int chkmin(T& a, const T& val) {return val < a ? a = val, 1 : 0;} template inline int chkmax(T& a, const T& val) {return a < val ? a = val, 1 : 0;} template inline T isqrt(T k) {T r = sqrt(k) + 1; while (r * r > k) r--; return r;} template inline T icbrt(T k) {T r = cbrt(k) + 1; while (r * r * r > k) r--; return r;} inline void addmod(int& a, int val, int p = MOD) {if ((a = (a + val)) >= p) a -= p;} inline void submod(int& a, int val, int p = MOD) {if ((a = (a - val)) < 0) a += p;} inline int mult(int a, int b, int p = MOD) {return (ll) a * b % p;} inline int inv(int a, int p = MOD) {return fpow(a, p - 2, p);} inline int sign(ld x) {return x < -EPS ? -1 : x > +EPS;} inline int sign(ld x, ld y) {return sign(x - y);} template struct FiniteField { T x; template T normalize(G x) { T p = mod().get(); if (x >= 0 && x < p) return x; x %= p; if (x < 0) x += p; else if (x >= p) x -= p; return x; } FiniteField() : x(0) {} template FiniteField(const G& y) { x = normalize(y); } FiniteField(const FiniteField& rhs) : x(rhs.x) { } template FiniteField operator = (const G& y) { x = normalize(y); return *this; } int operator == (const FiniteField& rhs) const { return x == rhs.x; } int operator != (const FiniteField& rhs) const { return x != rhs.x; } int operator < (const FiniteField& rhs) const { return x < rhs.x; } FiniteField operator ++(int) { T p = mod().get(); FiniteField res = *this; if ((++x) >= p) x -= p; return res; } FiniteField operator ++() { T p = mod().get(); if ((++x) >= p) x -= p; return *this; } FiniteField operator --(int) { T p = mod().get(); FiniteField res = *this; if ((--x) < 0) x += p; return res; } FiniteField operator --() { T p = mod().get(); if ((--x) < 0) x += p; return *this; } template FiniteField operator += (const G& y) { T p = mod().get(); if ((x += normalize(y)) >= p) x -= p; return *this; } template FiniteField operator -= (const G& y) { T p = mod().get(); if ((x -= normalize(y)) < 0) x += p; return *this; } FiniteField operator += (const FiniteField& rhs) { T p = mod().get(); if ((x += rhs.x) >= p) x -= p; return *this; } FiniteField operator -= (const FiniteField& rhs) { T p = mod().get(); if ((x -= rhs.x) < 0) x += p; return *this; } FiniteField operator + (const FiniteField& rhs) const { T p = mod().get(); FiniteField res; res.x = x + rhs.x; if (res.x >= p) res.x -= p; return res; } FiniteField operator - (const FiniteField& rhs) const { T p = mod().get(); FiniteField res; res.x = x - rhs.x; if (res.x < 0) res.x += p; return res; } template FiniteField operator *= (const G& y) { T p = mod().get(); x = mul()(x, normalize(y), p); return *this; } template FiniteField operator /= (const G& y) { T p = mod().get(); x = dvd()(x, normalize(y), p); return *this; } FiniteField operator *= (const FiniteField& rhs) { T p = mod().get(); x = mul()(x, rhs.x, p); return *this; } FiniteField operator /= (const FiniteField& rhs) { T p = mod().get(); x = dvd()(x, rhs.x, p); return *this; } template FiniteField operator * (const G& y) const { T p = mod().get(); FiniteField res; res.x = mul()(x, res.normalize(y), p); return res; } template FiniteField operator / (const G& y) const { T p = mod().get(); FiniteField res; res.x = dvd()(x, res.normalize(y), p); return res; } FiniteField operator * (const FiniteField& rhs) const { T p = mod().get(); FiniteField res; res.x = mul()(x, rhs.x, p); return res; } FiniteField operator / (const FiniteField& rhs) const { T p = mod().get(); FiniteField res; res.x = dvd()(x, rhs.x, p); return res; } template friend FiniteField operator * (const G& y, const FiniteField& rhs) { FiniteField res; res.x = res.normalize(y); return res * rhs; } template friend FiniteField operator / (const G& y, const FiniteField& rhs) { FiniteField res; res.x = res.normalize(y); return res / rhs; } template FiniteField operator ^= (G k) { T p = mod().get(); if (k == 0) { x = 1; return *this; } T t = x; k--; while (k > 0) { if (k & 1) x = mul()(x, t, p); t = mul()(t, t, p); k >>= 1; } return *this; } template FiniteField operator ^ (G k) const { T p = mod().get(); if (k == 0) return 1; T r = x, t = x; k--; while (k > 0) { if (k & 1) r = mul()(r, t, p); t = mul()(t, t, p); k >>= 1; } return r; } friend istream& operator >> (istream& is, FiniteField& rhs) { is >> rhs.x; rhs.x = rhs.normalize(rhs.x); return is; } friend ostream& operator << (ostream& os, const FiniteField& rhs) { os << rhs.x; return os; } }; template class mul { public: T operator () (const T& x, const T& y, const T& p) { return (long long) x * y % p; } }; template class dvd { public: T operator () (const T& x, const T& y, const T& p) { pair r = euclid(y, p); return mul()(x, (r.first % p + p) % p, p); } private: pair euclid(T a, T b) { if (b == 0) return make_pair(1, 0); pair r = euclid(b, a % b); return make_pair(r.second, r.first - a / b * r.second); } }; template class mod { public: T get() { return (T) 1e9 + 7; } }; typedef FiniteField, dvd, mod > FF; const int maxn = 1200 + 5; int n; int a[maxn]; int f[maxn][maxn]; FF fac[maxn]; FF ifac[maxn]; FF dp[maxn][maxn]; FF calc(int pos, int d) { if (pos == n) return 1; FF& res = dp[pos][d]; if (res != -1) return res; res = 0; FOR(k, 1, d + 1) if (f[pos][pos + k - 1]) { res += calc(pos + k, k) * ifac[d - k]; } res *= fac[d]; return res; } void solve() { fac[0] = 1; FOR(i, 1, maxn) fac[i] = fac[i - 1] * i; FOR(i, 0, maxn) ifac[i] = 1 / fac[i]; FOR(i, 0, maxn) FOR(j, 0, maxn) dp[i][j] = -1; cin >> n; FOR(i, 0, n) cin >> a[i], a[i]--; FOR(i, 0, n) { f[i][i] = 1; FOR(j, i + 1, n) { if (a[j] < a[j - 1]) break; f[i][j] = 1; } } FF res = 0; FOR(i, 1, n + 1) { if (f[0][i - 1]) { res += calc(i, i); } } cout << res << "\n"; } int main() { #ifdef _LOCAL_ freopen("in.txt", "r", stdin); //freopen("out.txt", "w", stdout); #else ios_base::sync_with_stdio(0); cin.tie(0); #endif solve(); cerr << "\nTime elapsed: " << 1.0 * clock() / CLOCKS_PER_SEC << "s\n"; return 0; }