//* #pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") //*/ #include // #include // #include using namespace std; // using namespace atcoder; // #define _GLIBCXX_DEBUG #define DEBUG(x) cerr << #x << ": " << x << endl; #define DEBUG_VEC(v) \ cerr << #v << ":"; \ for (int iiiiiiii = 0; iiiiiiii < v.size(); iiiiiiii++) \ cerr << " " << v[iiiiiiii]; \ cerr << endl; #define DEBUG_MAT(v) \ cerr << #v << endl; \ for (int iv = 0; iv < v.size(); iv++) { \ for (int jv = 0; jv < v[iv].size(); jv++) { \ cerr << v[iv][jv] << " "; \ } \ cerr << endl; \ } typedef long long ll; // #define int ll #define vi vector #define vl vector #define vii vector> #define vll vector> #define vs vector #define pii pair #define pis pair #define psi pair #define pll pair template pair operator+(const pair &s, const pair &t) { return pair(s.first + t.first, s.second + t.second); } template pair operator-(const pair &s, const pair &t) { return pair(s.first - t.first, s.second - t.second); } template ostream &operator<<(ostream &os, pair p) { os << "(" << p.first << ", " << p.second << ")"; return os; } #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define rep1(i, n) for (int i = 1; i <= (int)(n); i++) #define rrep(i, n) for (int i = (int)(n)-1; i >= 0; i--) #define rrep1(i, n) for (int i = (int)(n); i > 0; i--) #define REP(i, a, b) for (int i = a; i < b; i++) #define in(x, a, b) (a <= x && x < b) #define all(c) c.begin(), c.end() void YES(bool t = true) { cout << (t ? "YES" : "NO") << endl; } void Yes(bool t = true) { cout << (t ? "Yes" : "No") << endl; } void yes(bool t = true) { cout << (t ? "yes" : "no") << endl; } void NO(bool t = true) { cout << (t ? "NO" : "YES") << endl; } void No(bool t = true) { cout << (t ? "No" : "Yes") << endl; } void no(bool t = true) { cout << (t ? "no" : "yes") << endl; } template bool chmax(T &a, const T &b) { if (a < b) { a = b; return 1; } return 0; } template bool chmin(T &a, const T &b) { if (a > b) { a = b; return 1; } return 0; } #define UNIQUE(v) v.erase(std::unique(v.begin(), v.end()), v.end()); const ll inf = 1000000001; const ll INF = (ll)1e18 + 1; const long double pi = 3.1415926535897932384626433832795028841971L; int popcount(ll t) { return __builtin_popcountll(t); } // int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1}; // int dx2[8] = { 1,1,0,-1,-1,-1,0,1 }, dy2[8] = { 0,1,1,1,0,-1,-1,-1 }; vi dx = {0, 0, -1, 1}, dy = {-1, 1, 0, 0}; vi dx2 = {1, 1, 0, -1, -1, -1, 0, 1}, dy2 = {0, 1, 1, 1, 0, -1, -1, -1}; struct Setup_io { Setup_io() { ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0); cout << fixed << setprecision(25); } } setup_io; // const ll MOD = 1000000007; // const ll MOD = 998244353; // #define mp make_pair // #define endl '\n' vi aite; ll dfs(const string &s, int l, int r) { if (l >= r) { return 0; } if (l + 1 == r) { return 1; } int r2 = r - 1; int l2 = aite[r2]; ll ret = dfs(s, l2, r2); if (ret >= 62) { return INF; } ll ans = 1LL << ret; if (ans >= INF) { return ans; } ans += dfs(s, l + 1, l2 - 1); chmin(ans, INF); return ans; } signed main() { string s; cin >> s; int n = s.size(); stack st; aite.resize(n, -1); rrep(i, n) { if (s[i] == ')') { st.push(i); } else { if (st.empty()) { break; } aite[i] = st.top(); aite[st.top()] = i; st.pop(); } } int now = n - 1; ll ans = 0; while (now >= 0) { if (aite[now] == -1) { ans++; now = -1; break; } int r = now, l = aite[now]; ll tmp = dfs(s, l, r); ans += tmp; chmin(ans, INF); if (ans >= INF) { break; } now = l - 1; } if (ans >= INF) { cout << "INFTY" << endl; } else { cout << ans << endl; } }