Problem:
Score : 600 points

Problem Statement

A bracket sequence is a string that is one of the following:

An empty string;

The concatenation of (, A, and ) in this order, for some bracket sequence A ;

The concatenation of A and B in this order, for some non-empty bracket sequences A and B /

Given are N strings S_i. Can a bracket sequence be formed by concatenating all the N strings in some order?

Constraints

1 \leq N \leq 10^6

The total length of the strings S_i is at most 10^6.

S_i is a non-empty string consisting of ( and ).

Input

Input is given from Standard Input in the following format:

N
S_1
:
S_N

Output

If a bracket sequence can be formed by concatenating all the N strings in some order, print Yes; otherwise, print No.

Sample Input 1

2
)
(()

Sample Output 1

Yes

Concatenating (() and ) in this order forms a bracket sequence.

Sample Input 2

2
)(
()

Sample Output 2

No

Sample Input 3

4
((()))
((((((
))))))
()()()

Sample Output 3

Yes

Sample Input 4

3
(((
)
)

Sample Output 4

No

Solution in C++ (GCC 9.2.1) (judge verdict: Runtime Error)

/*
 * じょえチャンネル
 * 高評価・チャンネル登録よろしくおねがいします！
 * https://www.youtube.com/channel/UCRXsI3FL_kvaVL9zoolBfbQ
 */

#include <bits/stdc++.h>

//#pragma GCC target("avx2")
//#pragma GCC optimize("O3")
//#pragma GCC optimize("unroll-loops")

//here!!!
// define int long long !!!!!

#define int long long

// define int long long !!!!!

#define mod (int)((1e9) + 7)
//constexpr int mod = 998244353ll;

#ifdef int
#define inf (int)(3e18)
#else
#define inf (int)(5e8)
#endif

#define intt long long
#define itn long long
#define P pair<long long, long long>

#define rep(i, n) for (int i = 0; i < n; i++)
#define REP(i, n) for (int i = 1; i <= n; i++)
#define rev_rep(i, n) for (int i = n - 1; i >= 0; i--)
#define REV_REP(i, n) for (int i = n; i >= 1; i--)

#define ALL(v) v.begin(), v.end()

#define smallpriority_queue(x) priority_queue<x, vector<x>, greater<x>>

using namespace std;

//Library
//モッドパウ
inline int modpow(int x, int y, int m = mod) {
    int res = 1;
    while (y) {
        if (y & 1) {
            res *= x;
            res %= m;
        }
        x = x * x % m;
        y /= 2;
    }
    return res;
}

int mypow(int x, int y) {
    int res = 1;
    while (y) {
        if (y % 2) {
            res *= x;
        }
        x = x * x;
        y /= 2;
    }
    return res;
}
//is the number (x) a prime number?
bool prime(int x) {
    if (!x || x == 1) {
        return false;
    }
    for (int i = 2; i * i <= x; i++) {
        if (!(x % i)) {
            return false;
        }
    }
    return true;
}

//saidai-kouyakusuu
inline int gcd(int x, int y) {
    if (!y) {
        return x;
    }
    return gcd(y, x % y);
}

//number of keta
int keta(int x) {
    int ans = 0;
    while (x) {
        x /= 10;
        ans++;
    }
    return ans;
}

//sum of keta
int ketasum(int x) {
    int ans = 0;
    while (x) {
        ans += x % 10;
        x /= 10;
    }
    return ans;
}

inline int lcm(int x, int y) {
    int ans = x / gcd(x, y) * y;
    return ans;
}
int twobeki(int x) {
    int ans = 0;
    while (1) {
        if (!(x & 1)) {
            ans++;
            x >>= 1;
        } else {
            break;
        }
    }
    return ans;
}

template <class T, class U>
inline bool chmax(T &lhs, const U &rhs) {
    if (lhs < rhs) {
        lhs = rhs;
        return 1;
    }
    return 0;
}
template <class T, class U>
inline bool chmin(T &lhs, const U &rhs) {
    if (lhs > rhs) {
        lhs = rhs;
        return 1;
    }
    return 0;
}
void Yes() {
    cout << "Yes" << endl;
}
void No() {
    cout << "No" << endl;
}
void YES() {
    cout << "YES" << endl;
}
void NO() {
    cout << "NO" << endl;
}

#define fin(i) scanf("%lld", &i)
#define fout(i) printf("%lld", i)
#define fendl printf("\n")

int kai(int x, int y) {
    int res = 1;
    for (int i = x - y + 1; i <= x; i++) {
        res *= i;
        res %= mod;
    }
    return res;
}

int comb(int x, int y) {
    if (y > x)
        return 0;
    //    cout<<kai(x, y)<<' '<<modpow(kai(y, y), mod - 2)<<endl;
    return kai(x, y) * modpow(kai(y, y), mod - 2) % mod;
}
//Library-End

#define vecin(v)                       \
    for (int i = 0; i < v.size(); i++) \
        scanf("%lld", &v[i]);
#define vecout(v)                               \
    {                                           \
        for (int i = 0; i < (int)v.size(); i++) \
            printf("%lld ", v[i]);              \
        printf("\n");                           \
    }

template <typename T>
class kaageSegTree {
protected:
    unsigned int n = 1, rank = 0;
    std::vector<T> node;
    T nodee;
    virtual T nodef(const T &, const T &) const = 0;

public:
    kaageSegTree(unsigned int m, T init, T nodee) : nodee(nodee) {
        while (n < m) {
            n *= 2;
            rank++;
        }
        node.resize(2 * n);
        for (unsigned int i = n; i < 2 * n; i++)
            node[i] = init;
    }
    kaageSegTree(const std::vector<T> &initvec, T nodee) : nodee(nodee) {
        unsigned int m = initvec.size();
        while (n < m) {
            n *= 2;
            rank++;
        }
        node.resize(2 * n);
        for (unsigned int i = n; i < 2 * n; i++) {
            if (i - n < m)
                node[i] = initvec[i - n];
        }
    }
    virtual void update(int i, T x) {
        i += n;
        node[i] = x;
        while (i != 1) {
            i >>= 1;
            node[i] = nodef(node[2 * i], node[2 * i + 1]);
        }
    }
    virtual T query(int l, int r) {
        l += n;
        r += n;
        T ls = nodee, rs = nodee;
        while (l < r) {
            if (l & 1) {
                ls = nodef(ls, node[l]);
                l++;
            }
            if (r & 1) {
                r--;
                rs = nodef(node[r], rs);
            }
            l >>= 1;
            r >>= 1;
        }
        return nodef(ls, rs);
    }
    virtual T operator[](const int &x) {
        return node[n + x];
    }
    void fill(T x) {
        std::fill(ALL(node), x);
    }
    void print() {
        rep(i, n) std::cout << operator[](i) << " ";
        std::cout << std::endl;
    }
};
class RSQ : public kaageSegTree<int> {
    int nodef(const int &lhs, const int &rhs) const { return lhs + rhs; }

public:
    RSQ(int size, const int &def = 0) : kaageSegTree<int>(size, def, 0) {}
    RSQ(const std::vector<int> &initvec) : kaageSegTree<int>(initvec, 0) {}
};
class RMiQ : public kaageSegTree<int> {
    int nodef(const int &lhs, const int &rhs) const { return std::min(lhs, rhs); }

public:
    RMiQ(int size, const int &def = 0) : kaageSegTree<int>(size, def, inf) {}
    RMiQ(const std::vector<int> &initvec) : kaageSegTree<int>(initvec, inf) {}
};
class RMaQ : public kaageSegTree<int> {
    int nodef(const int &lhs, const int &rhs) const { return std::max(lhs, rhs); }

public:
    RMaQ(int size, const int &def = 0) : kaageSegTree<int>(size, def, -inf) {}
    RMaQ(const std::vector<int> &initvec) : kaageSegTree<int>(initvec, -inf) {}
};
template <typename T, typename U>
class IntervalSegTree : public kaageSegTree<T> {
protected:
    using kaageSegTree<T>::n;
    using kaageSegTree<T>::rank;
    using kaageSegTree<T>::node;
    using kaageSegTree<T>::nodef;
    using kaageSegTree<T>::nodee;
    std::vector<U> lazy;
    std::vector<bool> lazyflag;
    std::vector<int> width;
    virtual void lazyf(U &, const U &) = 0;
    virtual void updf(T &, const U &, const unsigned int &) = 0;
    void eval(int k) {
        for (int i = rank; i > 0; i--) {
            int nk = k >> i;
            if (lazyflag[nk]) {
                updf(node[2 * nk], lazy[nk], width[2 * nk]);
                updf(node[2 * nk + 1], lazy[nk], width[2 * nk + 1]);
                if (lazyflag[2 * nk])
                    lazyf(lazy[2 * nk], lazy[nk]);
                else
                    lazy[2 * nk] = lazy[nk];
                if (lazyflag[2 * nk + 1])
                    lazyf(lazy[2 * nk + 1], lazy[nk]);
                else
                    lazy[2 * nk + 1] = lazy[nk];
                lazyflag[2 * nk] = lazyflag[2 * nk + 1] = true;
                lazyflag[nk] = false;
            }
        }
    }

public:
    IntervalSegTree(unsigned int m, T init, T nodee) : kaageSegTree<T>(m, init, nodee) {
        lazy.resize(2 * n);
        lazyflag.resize(2 * n);
        width.resize(2 * n);
        width[1] = n;
        for (unsigned int i = 2; i < 2 * n; i++) {
            width[i] = width[i >> 1] >> 1;
        }
    }
    IntervalSegTree(T nodee, const std::vector<T> &initvec) : kaageSegTree<T>(initvec, nodee) {
        lazy.resize(2 * n);
        lazyflag.resize(2 * n);
        width.resize(2 * n);
        width[1] = n;
        for (unsigned int i = 2; i < 2 * n; i++) {
            width[i] = width[i >> 1] >> 1;
        }
    }
    void update(int i, U x) {
        i += n;
        eval(i);
        updf(node[i], x, width[i]);
        if (lazyflag[i])
            lazyf(lazy[i], x);
        else {
            lazyflag[i] = true;
            lazy[i] = x;
        }
        while (i /= 2)
            node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
    void update(int l, int r, U x) {
        l += n;
        r += n;
        int nl = l, nr = r;
        while (!(nl & 1))
            nl >>= 1;
        while (!(nr & 1))
            nr >>= 1;
        nr--;
        eval(nl);
        eval(nr);
        while (l < r) {
            if (l & 1) {
                updf(node[l], x, width[l]);
                if (lazyflag[l])
                    lazyf(lazy[l], x);
                else {
                    lazyflag[l] = true;
                    lazy[l] = x;
                }
                l++;
            }
            if (r & 1) {
                r--;
                updf(node[r], x, width[r]);
                if (lazyflag[r])
                    lazyf(lazy[r], x);
                else {
                    lazyflag[r] = true;
                    lazy[r] = x;
                }
            }
            l >>= 1;
            r >>= 1;
        }
        while (nl >>= 1)
            node[nl] = nodef(node[2 * nl], node[2 * nl + 1]);
        while (nr >>= 1)
            node[nr] = nodef(node[2 * nr], node[2 * nr + 1]);
    }
    T query(int l, int r) {
        l += n;
        r += n;
        eval(l);
        eval(r - 1);
        int ls = nodee, rs = nodee;
        while (l < r) {
            if (l & 1) {
                ls = nodef(ls, node[l]);
                l++;
            }
            if (r & 1) {
                r--;
                rs = nodef(node[r], rs);
            }
            l >>= 1;
            r >>= 1;
        }
        return nodef(ls, rs);
    }
    T operator[](const int &x) {
        eval(n + x);
        return node[n + x];
    }
    T queryForAll() {
        return node[1];
    }
};
class RAQRSQ : public IntervalSegTree<int, int> {
    int nodef(const int &a, const int &b) const { return a + b; }
    void lazyf(int &a, const int &b) { a += b; }
    void updf(int &a, const int &b, const unsigned int &width) { a += width * b; }

public:
    RAQRSQ(int size, const int &def = 0) : IntervalSegTree<int, int>(size, def, 0) {
        for (int i = n - 1; i > 0; i--)
            node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
    RAQRSQ(const std::vector<int> &initvec) : IntervalSegTree<int, int>((int)0, initvec) {
        for (int i = n - 1; i > 0; i--)
            node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
};
class RAQRMiQ : public IntervalSegTree<int, int> {
    int nodef(const int &a, const int &b) const { return std::min(a, b); }
    void lazyf(int &a, const int &b) { a += b; }
    void updf(int &a, const int &b, const unsigned int &width) { a += b; }

public:
    RAQRMiQ(int size, const int &def = 0) : IntervalSegTree<int, int>(size, def, inf) {
        for (int i = n - 1; i > 0; i--)
            node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
    RAQRMiQ(const std::vector<int> &initvec) : IntervalSegTree<int, int>(inf, initvec) {
        for (int i = n - 1; i > 0; i--)
            node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
};
class RAQRMaQ : public IntervalSegTree<int, int> {
    int nodef(const int &a, const int &b) const { return std::max(a, b); }
    void lazyf(int &a, const int &b) { a += b; }
    void updf(int &a, const int &b, const unsigned int &width) { a += b; }

public:
    RAQRMaQ(unsigned int size, const int &def = 0) : IntervalSegTree<int, int>(size, def, -inf) {
        for (int i = n - 1; i > 0; i--)
            node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
    RAQRMaQ(const std::vector<int> &initvec) : IntervalSegTree<int, int>(-inf, initvec) {
        for (int i = n - 1; i > 0; i--)
            node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
};
class RUQRSQ : public IntervalSegTree<int, int> {
    int nodef(const int &a, const int &b) const { return a + b; }
    void lazyf(int &a, const int &b) { a = b; }
    void updf(int &a, const int &b, const unsigned int &width) { a = width * b; }

public:
    RUQRSQ(int size, const int &def = 0) : IntervalSegTree<int, int>(size, def, 0) {
        for (int i = n - 1; i > 0; i--)
            node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
    RUQRSQ(const std::vector<int> &initvec) : IntervalSegTree<int, int>((int)0, initvec) {
        for (int i = n - 1; i > 0; i--)
            node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
};
class RUQRMiQ : public IntervalSegTree<int, int> {
    int nodef(const int &a, const int &b) const { return std::min(a, b); }
    void lazyf(int &a, const int &b) { a = b; }
    void updf(int &a, const int &b, const unsigned int &width) { a = b; }

public:
    RUQRMiQ(int size, const int &def = 0) : IntervalSegTree<int, int>(size, def, inf) {
        for (int i = n - 1; i > 0; i--)
            node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
    RUQRMiQ(const std::vector<int> &initvec) : IntervalSegTree<int, int>(inf, initvec) {
        for (int i = n - 1; i > 0; i--)
            node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
};
class RUQRMaQ : public IntervalSegTree<int, int> {
    int nodef(const int &a, const int &b) const { return std::max(a, b); }
    void lazyf(int &a, const int &b) { a = b; }
    void updf(int &a, const int &b, const unsigned int &width) { a = b; }

public:
    RUQRMaQ(int size, const int &def = 0) : IntervalSegTree<int, int>(size, def, -inf) {
        for (int i = n - 1; i > 0; i--)
            node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
    RUQRMaQ(const std::vector<int> &initvec) : IntervalSegTree<int, int>(-inf, initvec) {
        for (int i = n - 1; i > 0; i--)
            node[i] = nodef(node[2 * i], node[2 * i + 1]);
    }
};

////SegTree
//template <class T>
//class SegTree {
//    int n;                       // 葉の数
//    vector<T> node;              // データを格納するvector
//    T def;                       // 初期値かつ単位元
//    function<T(T, T)> operation; // 区間クエリで使う処理
//    function<T(T, T)> update;    // 点更新で使う処理
//
//    // 区間[a,b)の総和。ノードk=[l,r)に着目している。
//    T _query(int a, int b, int k, int l, int r) {
//        if (r <= a || b <= l) return def; // 交差しない
//        if (a <= l && r <= b)
//            return node[k]; // a,l,r,bの順で完全に含まれる
//        else {
//            T c1 = _query(a, b, 2 * k + 1, l, (l + r) / 2); // 左の子
//            T c2 = _query(a, b, 2 * k + 2, (l + r) / 2, r); // 右の子
//            return operation(c1, c2);
//        }
//    }
//
//public:
//    // _n:必要サイズ, _def:初期値かつ単位元, _operation:クエリ関数,
//    // _update:更新関数
//    SegTree(size_t _n, T _def, function<T(T, T)> _operation,
//            function<T(T, T)> _update)
//    : def(_def), operation(_operation), update(_update) {
//        n = 1;
//        while (n < _n) {
//            n *= 2;
//        }
//        node = vector<T>(2 * n , def);
//    }
//
//    // 場所i(0-indexed)の値をxで更新
//    void change(int i, T x) {
//        i += n - 1;
//        node[i] = update(node[i], x);
//        while (i > 0) {
//            i = (i - 1) / 2;
//            node[i] = operation(node[i * 2 + 1], node[i * 2 + 2]);
//        }
//    }
//
//    // [a, b)の区間クエリを実行
//    T query(int a, int b) {
//        return _query(a, b, 0, 0, n);
//    }
//
//    // 添字でアクセス
//    T operator[](int i) {
//        return node[i + n - 1];
//    }
//};

template <class T>
class SegTree {
    int n;
    vector<T> node;
    T def;
    function<T(T, T)> operation;
    function<T(T, T)> update;

public:
    SegTree(unsigned int _n, T _def, function<T(T, T)> _operation,
            function<T(T, T)> _update)
        : def(_def), operation(_operation), update(_update) {
        n = 1;
        while (n < _n) {
            n *= 2;
        }
        node = vector<T>(n * 2, def);
    }
    SegTree(vector<int> &initvec, function<T(T, T)> _operation,
            function<T(T, T)> _update)
        : operation(_operation), update(_update) {
        n = 1;
        while (n < initvec.size()) {
            n *= 2;
        }
        node = vector<T>(n * 2, def);
        for (int i = n; i < n + initvec.size(); i++) {
            node[i] = initvec[i - n];
        }
        for (int i = n - 1; i >= 1; i--) {
            node[i] = operation(node[i * 2], node[i * 2 + 1]);
        }
    }
    void change(int i, T x) {
        i += n;
        node[i] = update(node[i], x);
        while (i >= 1) {
            i >>= 1;
            node[i] = operation(node[i * 2], node[i * 2 + 1]);
        }
    }
    T query(int l, int r) {
        l += n;
        r += n;
        T rx = def, lx = def;
        while (l < r) {
            if (l & 1) {
                lx = operation(lx, node[l]);
                l++;
            }
            if (r & 1) {
                r--;
                rx = operation(node[r], rx);
            }
            l >>= 1;
            r >>= 1;
        }
        return operation(lx, rx);
    }
    T operator[](const int &x) {
        return node[x + n];
    }
    void fill(T x) {
        std::fill(ALL(node), x);
    }
    void print() {
        rep(i, n) std::cout << operator[](i) << " ";
        std::cout << std::endl;
    }
};

class Union_Find {
    vector<int> par;
    vector<int> rankmy;
    vector<int> ookisa;

public:
    Union_Find(int size) {
        par = vector<int>(size);
        rankmy = vector<int>(size);
        ookisa = vector<int>(size);
        for (int i = 0; i < size; i++) {
            par[i] = i;
            ookisa[i] = 1;
        }
    }

    int find(int x) {
        if (par[x] == x) {
            return x;
        }
        return par[x] = find(par[x]);
    }

    void unite(int x, int y) {
        x = find(x);
        y = find(y);
        if (x == y) {
            return;
        }
        if (rankmy[x] < rankmy[y]) {
            par[x] = y;
            ookisa[y] += ookisa[x];
            ookisa[x] = 0;
        } else {
            par[y] = x;
            ookisa[x] += ookisa[y];
            ookisa[y] = 0;
            if (rankmy[x] == rankmy[y]) {
                rankmy[x]++;
            }
        }
    }
    int size(int i) {
        i = find(i);
        return ookisa[i];
    }
    bool same(int x, int y) {
        return find(x) == find(y);
    }
};

class BIT {
    vector<int> data;
    int size = 0;

public:
    BIT(int _size) {
        data = vector<int>(_size + 1);
        size = _size;
    }
    void add(int i, int x) {
        while (i <= size) {
            data[i] += x;
            i += i & -i;
        }
    }
    int sum(int i) {
        assert(i <= size);
        int s = 0;
        while (i > 0) {
            s += data[i];
            i -= i & -i;
        }
        return s;
    }
    int lower_bound(int x) {
        if (x <= 0) {
            return 0;
        } else {
            int i = 0;
            int r = 1;
            while (r < size)
                r = r << 1;
            for (int len = r; len > 0; len = len >> 1) {
                if (i + len < size && data[i + len] < x) {
                    x -= data[i + len];
                    i += len;
                }
            }
            return i + 1;
        }
    }
};

//Union-Find-End

int perm[2000005];
void init_perm() {
    perm[0] = 1;
    REP(i, 2000004) {
        perm[i] = perm[i - 1] * i % mod;
    }
}

int nCk(int x, int y) {
    if (y > x) {
        return 0;
    }
    if (x < 0) {
        return 0;
    }
    return perm[x] * modpow(perm[x - y], mod - 2) % mod * modpow(perm[y], mod - 2) % mod;
}

double kyori(pair<int, int> f, pair<int, int> s) {
    double ans = 0;
    double t = fabs(f.first - s.first);
    double y = fabs(f.second - s.second);
    ans = sqrt(t * t + y * y);
    return ans;
}

inline string stringmax(string &x, string &y) {
    if (x.size() > y.size()) {
        return x;
    }
    if (x.size() < y.size()) {
        return y;
    }
    rep(i, x.size()) {
        if (x[i] > y[i]) {
            return x;
        }
        if (x[i] < y[i]) {
            return y;
        }
    }
    return x;
}

vector<int> RollingHash(string &s, string &t) {
    vector<int> ans;
    __int128 h = 0, hamod = 0, ki = 0, kim = 0, hikaku = 0, one = 0;
    one = 1;
    ki = 1000000007ll;
    hamod = (one << 61) - 1;
    kim = 1;
    rep(i, t.size()) {
        hikaku *= ki;
        h *= ki;
        kim *= ki;
        hikaku += t[i];
        h += s[i];
        hikaku %= hamod;
        h %= hamod;
        kim %= hamod;
    }
    rep(i, (int)s.size() - (int)t.size() + 1) {
        if (h == hikaku) {
            ans.emplace_back(i);
        }
        h *= ki;
        h %= hamod;
        h += s[i + (int)t.size()];
        h %= hamod;
        h += hamod;
        h -= s[i] * kim % hamod;
        h %= hamod;
    }
    return ans;
}
struct edge {
    int to;
    int length;
    edge(int _to, int _length) {
        to = _to;
        length = _length;
    }
};
vector<int> djkstra(vector<vector<edge>> &road, int start) {
    vector<int> kyo(road.size(), inf);
    smallpriority_queue(P) q;
    q.push({0, start});
    kyo[start] = 0;
    while (q.size()) {
        int x = q.top().second;
        itn now = q.top().first;
        q.pop();
        if (kyo[x] < now) {
            continue;
        }
        for (auto &i : road[x]) {
            if (kyo[i.to] > now + i.length) {
                kyo[i.to] = now + i.length;
                q.push({kyo[i.to], i.to});
            }
        }
    }
    return kyo;
}

#define R_MIN ([](long long a, long long b) { return min(a, b); })
#define R_MAX ([](P a, P b) { return max(a, b); })
#define R_SUM ([](long long a, long long b) { return a + b; })

#define NORMAL_UPDATE ([](P a, P b) { return b; })
#define ADD_UPDATE ([](long long a, long long b) { return a + b; })
#define MINUS_UPDATE ([](long long a, long long b) { return a - b; }

#define endl "\n" //interactive の時に注意！！！
#define printd cout << fixed << setprecision(10)
#define rrep(i, f, s) for (int i = f; i < s; i++)
#define RREP(i, f, s) for (int i = f; i <= s; i++)
#define rev_rrep(i, f, s) for (int i = s - 1; i >= f; i--)
#define REV_RREP(i, f, s) for (int i = s; i >= f; i--)

int n, l, r;
string s[1000004];
itn sm[1000004], c[1000004];
set<pair<P, string>> st;
map<int, int> mp;
priority_queue<int> q[1000004];
signed main() {
    ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
    cin >> n;

    rep(i, n) {
        cin >> s[i];
        sm[i] = inf;
        rep(j, s[i].size()) {
            if (s[i][j] == '(') {
                c[i]++;
                l++;
                chmin(sm[i], c[i]);
            } else {
                c[i]--;
                r++;
                chmin(sm[i], c[i]);
            }
        }
        mp[sm[i]] = 1;
    }
    if (l != r) {
        No();
        return 0;
    }
    int cnt = 0;
    for (auto &i : mp) {
        i.second = cnt;
        cnt++;
    }
    P p = {-inf, -1};
    SegTree<P> seg(n + 1, p, R_MAX, NORMAL_UPDATE);
    rep(i, n) {
        q[mp[sm[i]]].push(c[i]);
    }
    rep(i, n) {
        if (q[i].size()) {
            seg.change(i, {q[i].top(), i});
            //            cout<<q[i].top()<<' '<<i<<endl;
            //            cout<<seg[i].second<<endl;
        }
    }
    int now = 0;
    rep(i, n) {
        auto k = mp.lower_bound(-now);
        if (k == mp.end()) {
            No();
            return 0;
        }
        int f = k->second;
        P x = seg.query(f, n);
        if (x.second == -1 || x.first == -inf) {
            //            cout<<seg[0].second<<endl;
            No();
            return 0;
        }
        now += x.first;
        q[x.second].pop();
        if (q[x.second].size()) {
            seg.change(x.second, {q[x.second].top(), i});
        } else {
            seg.change(x.second, {-inf, -1});
        }
    }
    Yes();
}