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#line 1 "test/aoj_1322.test.cpp"
#define PROBLEM "http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=1322"
#include <cstdio>
#include <cassert>
#include <cctype>
#include <algorithm>
#include <string>
#include <vector>
#line 1 "ModularArithmetic/modint.cpp"
/**
* @brief 合同算術用クラス
* @author えびちゃん
*/
#include <cstdint>
#include <limits>
#include <type_traits>
#include <utility>
template <intmax_t Modulo>
class modint {
public:
using value_type = typename std::conditional<
(0 < Modulo && Modulo < std::numeric_limits<int>::max() / 2), int, intmax_t
>::type;
private:
static constexpr value_type S_cmod = Modulo; // compile-time
static value_type S_rmod; // runtime
value_type M_value = 0;
static constexpr value_type S_inv(value_type n, value_type m) {
value_type x = 0;
value_type y = 1;
value_type a = n;
value_type b = m;
for (value_type u = y, v = x; a;) {
value_type q = b / a;
std::swap(x -= q*u, u);
std::swap(y -= q*v, v);
std::swap(b -= q*a, a);
}
if ((x %= m) < 0) x += m;
return x;
}
static value_type S_normalize(intmax_t n, value_type m) {
if (n >= m) {
n %= m;
} else if (n < 0) {
if ((n %= m) < 0) n += m;
}
return n;
}
public:
modint() = default;
modint(intmax_t n): M_value(S_normalize(n, get_modulo())) {}
modint& operator =(intmax_t n) {
M_value = S_normalize(n, get_modulo());
return *this;
}
modint& operator +=(modint const& that) {
if ((M_value += that.M_value) >= get_modulo()) M_value -= get_modulo();
return *this;
}
modint& operator -=(modint const& that) {
if ((M_value -= that.M_value) < 0) M_value += get_modulo();
return *this;
}
modint& operator *=(modint const& that) {
intmax_t tmp = M_value;
tmp *= that.M_value;
M_value = tmp % get_modulo();
return *this;
}
modint& operator /=(modint const& that) {
intmax_t tmp = M_value;
tmp *= S_inv(that.M_value, get_modulo());
M_value = tmp % get_modulo();
return *this;
}
modint& operator ++() {
if (++M_value == get_modulo()) M_value = 0;
return *this;
}
modint& operator --() {
if (M_value-- == 0) M_value = get_modulo()-1;
return *this;
}
modint operator ++(int) { modint tmp(*this); ++*this; return tmp; }
modint operator --(int) { modint tmp(*this); --*this; return tmp; }
friend modint operator +(modint lhs, modint const& rhs) { return lhs += rhs; }
friend modint operator -(modint lhs, modint const& rhs) { return lhs -= rhs; }
friend modint operator *(modint lhs, modint const& rhs) { return lhs *= rhs; }
friend modint operator /(modint lhs, modint const& rhs) { return lhs /= rhs; }
modint operator +() const { return *this; }
modint operator -() const {
if (M_value == 0) return *this;
return modint(get_modulo() - M_value);
}
friend bool operator ==(modint const& lhs, modint const& rhs) {
return lhs.M_value == rhs.M_value;
}
friend bool operator !=(modint const& lhs, modint const& rhs) {
return !(lhs == rhs);
}
value_type get() const { return M_value; }
static value_type get_modulo() { return ((S_cmod > 0)? S_cmod: S_rmod); }
template <int M = Modulo, typename Tp = typename std::enable_if<(M <= 0)>::type>
static Tp set_modulo(value_type m) { S_rmod = m; }
};
template <intmax_t N>
constexpr typename modint<N>::value_type modint<N>::S_cmod;
template <intmax_t N>
typename modint<N>::value_type modint<N>::S_rmod;
#line 1 "ModularArithmetic/operations.cpp"
/**
* @brief 合同算術の基本演算
* @author えびちゃん
*/
#include <stdexcept>
#line 11 "ModularArithmetic/operations.cpp"
#line 1 "integer/bit.cpp"
/**
* @brief ビット演算
* @author えびちゃん
*/
// XXX integral promotion 関連の注意をあまりしていません
#include <climits>
#include <type_traits>
template <typename Tp>
constexpr auto countl_zero(Tp n)
-> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
using value_type = typename std::make_unsigned<Tp>::type;
int bits = (sizeof(value_type) * CHAR_BIT);
if (n == 0) return bits;
int res = 0;
for (int i = bits / 2; i > 0; i /= 2) {
value_type mask = ((static_cast<value_type>(1) << i) - 1) << i;
if (n & mask) n >>= i;
else res += i;
}
return res;
}
template <typename Tp>
constexpr auto countl_one(Tp n)
-> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
using value_type = typename std::make_unsigned<Tp>::type;
return countl_zero(static_cast<value_type>(~n));
}
template <typename Tp>
constexpr auto countr_zero(Tp n)
-> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
using value_type = typename std::make_unsigned<Tp>::type;
int bits = (sizeof(value_type) * CHAR_BIT);
if (n == 0) return bits;
int res = 0;
for (int i = bits / 2; i > 0; i /= 2) {
value_type mask = ((static_cast<value_type>(1) << i) - 1);
if (!(n & mask)) res += i, n >>= i;
}
return res;
}
template <typename Tp>
constexpr auto countr_one(Tp n)
-> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
using value_type = typename std::make_unsigned<Tp>::type;
return countr_zero(static_cast<value_type>(~n));
}
constexpr unsigned long long half_mask[] = {
0x5555555555555555uLL, 0x3333333333333333uLL, 0x0F0F0F0F0F0F0F0FuLL,
0x00FF00FF00FF00FFuLL, 0x0000FFFF0000FFFFuLL, 0x00000000FFFFFFFFuLL
};
template <typename Tp>
constexpr auto popcount(Tp n)
-> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
int bits = static_cast<int>((sizeof n) * CHAR_BIT);
for (int i = 0, j = 1; j < bits; ++i, j *= 2) {
if (j <= 8) n = (n & half_mask[i]) + ((n >> j) & half_mask[i]);
else n += n >> j;
}
return n & 0xFF;
}
template <typename Tp>
constexpr auto parity(Tp n)
-> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{ return popcount(n) & 1; }
template <typename Tp>
int clz(Tp n) { return countl_zero(static_cast<typename std::make_unsigned<Tp>::type>(n)); }
template <typename Tp>
int ctz(Tp n) { return countr_zero(static_cast<typename std::make_unsigned<Tp>::type>(n)); }
template <typename Tp>
int ilog2(Tp n) {
return (CHAR_BIT * sizeof(Tp) - 1) - clz(static_cast<typename std::make_unsigned<Tp>::type>(n));
}
template <typename Tp>
bool is_pow2(Tp n) { return (n > 0) && ((n & (n-1)) == 0); }
template <typename Tp>
Tp floor2(Tp n) { return is_pow2(n)? n: static_cast<Tp>(1) << ilog2(n); }
template <typename Tp>
Tp ceil2(Tp n) { return is_pow2(n)? n: static_cast<Tp>(2) << ilog2(n); }
template <typename Tp>
constexpr auto reverse(Tp n)
-> typename std::enable_if<std::is_unsigned<Tp>::value, Tp>::type
{
int bits = static_cast<int>((sizeof n) * CHAR_BIT);
for (int i = 0, j = 1; j < bits; ++i, j *= 2) {
n = ((n & half_mask[i]) << j) | ((n >> j) & half_mask[i]);
}
return n;
}
#line 13 "ModularArithmetic/operations.cpp"
template <typename ModInt>
ModInt pow(ModInt const& n, intmax_t iexp) {
ModInt res(1);
for (ModInt dbl = n; iexp; iexp >>= 1) {
if (iexp & 1) res *= dbl;
dbl *= dbl;
}
return res;
}
template <typename ModInt>
ModInt sqrt(ModInt const& n) {
if (n == 0) return n;
using value_type = typename ModInt::value_type;
intmax_t const p = n.get_modulo();
if (p % 4 == 3) {
ModInt r = pow(n, (p+1) / 4);
if (r * r == n) return r;
throw std::logic_error("quadratic nonresidue");
}
value_type s = ctz(p-1);
value_type q = (p-1) >> s;
ModInt z;
for (value_type z0 = 2; z0 < p; ++z0) {
z = ModInt(z0);
if (pow(z, (p-1) / 2) == -1) break;
}
value_type m = s;
ModInt c = pow(z, q);
ModInt t = pow(n, q);
ModInt r = pow(n, (q+1) / 2);
while (true) {
if (t == 0) return 0;
if (t == 1) return r;
value_type i = 0;
for (auto tt = t; tt != 1; ++i) tt *= tt;
if (i == m) throw std::logic_error("quadratic nonresidue");
auto b = c;
for (value_type j = 0; j < m-i-1; ++j) b *= b;
m = i;
c = b * b;
t *= c;
r *= b;
}
}
template <typename ModInt>
std::vector<ModInt> sqrt_all(ModInt const& n) {
try {
auto r = sqrt(n);
if (r == -r) return {r};
return {r, -r};
} catch (std::logic_error const&) {
return {};
}
}
template <typename ModPolynomial>
ModPolynomial log(ModPolynomial const& f) {
auto g = f;
g.differentiate();
g *= f.inverse(f.degree()+1);
g.integrate();
return g;
}
#line 12 "test/aoj_1322.test.cpp"
using mi = modint<2011>;
std::vector<std::string> ops{"+-", "*"};
mi parse(std::vector<std::string> const& s, size_t& l, size_t u, size_t b, size_t preced = 0) {
size_t base;
bool found = false;
while (!found) {
for (base = u; base < b; ++base) {
if (s[base][l] != '.') {
found = true;
break;
}
}
if (!found) ++l;
}
if (preced == ops.size()) {
mi res;
if (s[base][l] == '(') {
++l;
assert(s[base][l] == '.');
res = parse(s, ++l, u, b, 0);
assert(s[base][l] == '.');
++l;
assert(s[base][l] == ')');
++l;
} else if (isdigit(s[base][l])) {
res = s[base][l++] - '0';
} else if (s[base][l] == '-' && s[base][l+1] == '.') {
res = -parse(s, l += 2, u, b, preced);
} else if (s[base][l] == '-' && s[base][l+1] == '-') {
size_t ln = l;
size_t ld = l;
res = parse(s, ln, u, base, 0) / parse(s, ld, base+1, b, 0);
while (s[base][l] == '-') ++l;
}
if (base-1 < s.size() && l < s[base-1].length() && isdigit(s[base-1][l]))
res = pow(res, s[base-1][l++]-'0');
return res;
}
mi res = parse(s, l, u, b, preced+1);
while (l < s[base].length()) {
assert(s[base][l] == '.');
char op = s[base][l+1];
if (!std::count(ops[preced].begin(), ops[preced].end(), op)) break;
l += 2;
assert(s[base][l] == '.');
mi cur = parse(s, ++l, u, b, preced+1);
if (op == '+') res += cur;
if (op == '-') res -= cur;
if (op == '*') res *= cur;
}
return res;
}
int testcase_ends() {
size_t n;
scanf("%zu", &n);
if (n == 0) return 1;
std::vector<std::string> s(n);
for (auto& si: s) {
char buf[96];
scanf("%s", buf);
si = buf;
}
size_t l = 0;
printf("%d\n", parse(s, l, 0, n).get());
return 0;
}
int main() {
while (!testcase_ends()) {}
}