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;
typedef long long ll;
typedef long double ld;
const int M = 1000007;
int add(int a, int b) {
a += b;
if (a >= M) return a - M;
if (a < 0) return a + M;
return a;
}
int mul(int a, int b) {
return a * (ll) b % M;
}
void addup(int &a, int b) {
a = add(a, b);
}
void mulup(int &a, int b) {
a = mul(a, b);
}
const int N = 10000 + 7;
int n, a[N], mx = 0, ways[N][N]; /// ways[length left][current max]
signed main() {
ios::sync_with_stdio(0); cin.tie(0);
/// freopen ("input.txt", "r", stdin);
cin >> n;
for (int i = 1; i <= n; i++) {
cin >> a[i];
if (a[i] > mx) {
assert(a[i] == mx + 1);
mx = a[i];
}
}
for (int mx = 1; mx <= n; mx++) {
ways[0][mx] = 1;
}
for (int len = 1; len <= n; len++) {
for (int mx = 1; mx <= n; mx++) {
/// ways[len][mx]
ways[len][mx] = add(mul(mx, ways[len - 1][mx]), ways[len - 1][mx + 1]);
}
}
int sol = 1;
mx = 0;
for (int i = 1; i <= n; i++) {
for (int pl = 1; pl < a[i]; pl++) {
addup(sol, ways[n - i][mx]);
}
mx = max(mx, a[i]);
}
cout << sol << "\n";
}
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