This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
#define REP(i, j, k) for (int i = j; i < k; i++)
#define RREP(i, j, k) for (int i = j; i >= k; i--)
template<class T>
inline bool mxto(T &a, T b) {return a < b ? a = b, 1 : 0;}
template<class T>
inline bool mnto(T &a, T b) {return a > b ? a = b, 1 : 0;}
typedef long long ll;
#define FI first
#define SE second
#define MP make_pair
typedef pair<int, int> ii;
#define pb push_back
#define ALL(x) x.begin(), x.end()
typedef vector<int> vi;
typedef vector<ii> vii;
#define MT make_tuple
typedef tuple<int, int, int> iii;
#ifndef DEBUG
#define cerr if (0) cerr
#endif
#define INF 1000000005
#define LINF 1000000000000000005ll
#define MAXN 10005
#define MOD 1000007
int n;
int a[MAXN];
struct hsh {
int operator() (const iii& o) const {
auto [a, b, c] = o;
return (a << 4) + (b << 2) + c;
}
};
unordered_map<iii, int, hsh> memo;
int dp(int i, int j, bool same) {
if (i >= n) {
return 1;
}
if (memo.find(MT(i, j, same)) != memo.end()) {
return memo[MT(i, j, same)];
}
int res = 0;
if (same) {
res += (ll) dp(i + 1, j, 0) * min(j, a[i] - 1) % MOD;
if (res >= MOD) {
res -= MOD;
}
if (a[i] <= j + 1) {
res += dp(i + 1, max(j, a[i]), 1);
if (res >= MOD) {
res -= MOD;
}
}
} else {
res += (ll) dp(i + 1, j, 0) * j % MOD;
if (res >= MOD) {
res -= MOD;
}
res += dp(i + 1, j + 1, 0);
if (res >= MOD) {
res -= MOD;
}
}
return memo[MT(i, j, same)] = res;
}
int main() {
#ifndef DEBUG
ios::sync_with_stdio(0), cin.tie(0);
#endif
cin >> n;
REP (i, 0, n) {
cin >> a[i];
}
cout << dp(0, 0, 1) << '\n';
return 0;
}
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