#include <bits/stdc++.h>
using namespace std;
/* Merge 2 vector thanh 1
merge(Tree[2 * id].begin(), Tree[2 * id].end(),
Tree[2 * id + 1].begin(), Tree[2 * id + 1].end(),
back_inserter(Tree[id]));
*/
/*legendry
int legendry(int n, int p)
{
int ans = 0, x = 1;
while (x * p <= n)
{
x *= p;
ans += n/x;
}
return ans;
}
*/
/* Phi ham euler
int Phi(int x)
{
int res = 0;
for (int i = 2; i <= sqrt(x); i++)
{
if (x % i == 0)
{
res -= res / i;
while (x % i == 0)
{
x /= i;
}
}
}
if (x > 1) res -= res / x;
return res;
}
int phi[N];
void sang(int x)
{
fu(i, 1, x) phi[i] = i;
fu(i, 2, x)
{
if (phi[i] == i)
{
for (int j = i; j <= x; j += i)
{
phi[j] -= phi[j] / i;
}
}
}
}
*/
/* To Hop
const int MAX = 2e5 + 1;
int powmod(int a, int b)
{
if (b == 0) return 1;
else if (b == 1) return a % MOD;
int vl = powmod(a, b/2);
if (b % 2 == 0) return vl * vl % MOD;
return 1ll * (vl * vl % MOD) * (a % MOD) % MOD;
}
void preComb()
{
frac[0] = 1;
fu(i,1,MAX) frac[i] = 1LL * frac[i - 1] * i % MOD;
finv[MAX] = powmod(frac[MAX], MOD - 2);
fd(i,MAX,1) finv[i - 1] = 1LL * finv[i] * i % MOD;
}
int Comb(int k, int n)
{
return k > n ? 0 : 1LL * frac[n] * finv[k] % MOD * finv[n - k] % MOD;
}
*/
/* Fenwick 2d
struct Fenwick2D
{
vector<vector<int>> Tree;
int m, n;
Fenwick2D(int _m = 0, int _n = 0)
{
m = _m;
n = _n;
Tree.resize(m + 1);
fu(i,0,m)
{
Tree[i].resize(n + 1);
fill(Tree[i].begin(), Tree[i].end(), 0);
}
}
void update(int x, int y, int vl)
{
for(int i = x; i <= m; i += i&-i)
{
for(int j = y; j <= n; j += j&-j)
{
Tree[i][j] += vl;
}
}
}
int get(int x, int y)
{
int res = 0;
for(int i = x; i > 0; i -= i&-i)
{
for(int j = y; j > 0; j -= j&-j)
{
res += Tree[i][j];
}
}
return res;
}
} F2D;
*/
/* HLD
void dfs(int u, int p)
{
child[u] = 1;
for (int v : adj[u]) if (v != p)
{
par[v] = u;
depth[v] = depth[u] + 1;
dfs(v, u);
child[u] += child[v];
}
}
int lca(int u, int v)
{
while(ChainId[u] != ChainId[v])
{
if(ChainId[u] > ChainId[v])
{
u = par[head[ChainId[u]]];
}
else
{
v = par[head[ChainId[v]]];
}
}
if(depth[u] < depth[v]) return u;
return v;
}
void hld(int u, int p)
{
if (!head[CurChain]) head[CurChain] = u;
ChainId[u] = CurChain;
Pos[u] = ++CurPos;
Arr[CurPos] = v[u];
int MaxNode = 0;
for(int v : adj[u]) if (v != p)
{
if (child[v] > child[MaxNode]) MaxNode = v;
}
if (MaxNode) hld(MaxNode, u);
for(int v : adj[u]) if (v != p && v != MaxNode)
{
CurChain++;
hld(v, u);
}
}
int Query(int u, int v)
{
int Lca = lca(u, v);
int ans = LLONG_MIN;
while (ChainId[u] != ChainId[Lca])
{
maximize(ans, S.query(1,1,CurPos,Pos[head[ChainId[u]]], Pos[u]));
u = par[head[ChainId[u]]];
}
while (ChainId[v] != ChainId[Lca])
{
maximize(ans, S.query(1,1,CurPos,Pos[head[ChainId[v]]], Pos[v]));
v = par[head[ChainId[v]]];
}
if (depth[u] < depth[v])
{
maximize(ans, S.query(1,1,CurPos,Pos[u],Pos[v]));
}else maximize(ans, S.query(1,1,CurPos,Pos[v],Pos[u]));
return ans;
}
*/
/*
Convex Hull Trick Min
int pointer;
vector<ll> M;
vector<ll> B;
bool bad(int l1,int l2,int l3)
{
return (B[l3] - B[l1]) * (M[l1] - M[l2]) < (B[l2] - B[l1]) * (M[l1] - M[l3]);
}
void add(ll m,ll b)
{
M.push_back(m);
B.push_back(b);
while (M.size() >= 3 && bad(M.size() - 3, M.size() - 2, M.size() - 1))
{
M.erase(M.end()-2);
B.erase(B.end()-2);
}
}
ll query(ll x)
{
if (pointer >= M.size())
pointer = M.size() - 1;
while (pointer < M.size() - 1 && M[pointer+1] * x + B[pointer+1] < M[pointer] * x + B[pointer])
pointer++;
return M[pointer] * x + B[pointer];
}
*/
/* TRIE
struct Trie
{
struct Node
{
bool isEnd;
Node *child[26];
Node()
{
fu(i,0,25) child[i] = nullptr;
isEnd = 0;
}
};
Node *root = new Node();
void add(string str)
{
Node *x = root;
fu(i,0,str.size()-1)
{
int c = str[i] - 'a';
if (x->child[c] == nullptr) x->child[c] = new Node();
x = x->child[c];
}
x->isEnd = 1;
}
bool query(string str)
{
Node *x = root;
fu(i,0,str.size()-1)
{
int c = str[i] - 'a';
if (x->child[c] == nullptr) return false;
else x = x->child[c];
}
return (x->isEnd == 1);
}
} T;
*/
/* KMP
int kmp[N], match[N];
void cre_kmp()
{
int k = kmp[1] = 0;
fu(i,2,m)
{
while (k > 0 && B[i] != B[k+1]) k = kmp[k];
kmp[i] = B[i] == B[k+1] ? ++k : 0;
}
}
void cre_match()
{
int k = 0;
fu(i,1,n)
{
while(k > 0 && A[i] != B[k+1]) k = kmp[k];
match[i] = A[i] == B[k+1] ? ++k : 0;
if (match[i] == m) cout<<i - m + 1<<sp;
}
}
*/
/* CHIA CAN
fu(i,1,q)
{
int t; cin>>t;
if (t == 1)
{
int u, v; cin>>u>>v;
auto it = blck[u/sq].lower_bound(a[u]);
blck[u/sq].erase(it);
a[u] = v;
blck[u/sq].insert(a[u]);
}
else
{
int L, R, k; cin>>L>>R>>k;
int res = INT_MAX;
int blockL = (L - 1) / sq + 1;
int blockR = R / sq - 1;
fu(i,blockL,blockR)
{
auto it = blck[i].lower_bound(k);
if (it != blck[i].end()) minimize(res, *it);
}
if (L/sq != R/sq)
{
fu(i,L,blockL*sq-1) if (a[i] >= k) minimize(res, a[i]);
fu(i,(blockR+1)*sq,R) if (a[i] >= k) minimize(res, a[i]);
}
else fu(i,L,R) if (a[i] >= k) minimize(res, a[i]);
cout<<(res == INT_MAX ? -1 : res)<<el;
}
}
*/
/* DIJSKTRA
void dijkstra(int st)
{
d[st] = 0;
priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> q;
q.push({0,st});
while (!q.empty())
{
pair<l, int> tmp = q.top();
q.pop();
int u = tmp.second;
int w = tmp.first;
if (w > d[u]) continue;
for (auto it : adj[u])
{
int v = it.first;
int c = it.second;
if (maximize(d[v], w + c))
{
q.push({d[v], v});
}
}
}
}
/* FENWICK TREE
struct Fenwick
{
vector<pair<ll, int>> Tree;
int n;
Fenwick(int _n = 0)
{
n = _n;
Tree.resize(n+1);
}
void update(ll x, ll vl)
{
for(;x<=n;x+=x&-x)
{
Tree[x].first+=vl;
Tree[x].second++;
}
}
pair<ll,int> get(ll x)
{
pair<ll, int> tmp;
for(;x;x-=x&-x)
{
tmp.first += Tree[x].first;
tmp.second += Tree[x].second;
}
return tmp;
}
pair<ll,int> query(int l, int r)
{
if (l == 0) return get(r);
return {get(r).first - get(l-1).first, get(r).se - get(l-1).se};
}
} F;
/* SEGMENT TREE
struct Segment
{
struct Node
{
ll vl, lz;
Node(ll _vl = 0, ll _lz = 0)
{
vl = _vl;
lz = _lz;
}
};
vector<Node> Tree;
int n;
Segment(int _n = 0)
{
n = _n;
Tree.resize(4*n+1);
}
void build(int id, int l, int r)
{
if (l == r)
{
Tree[id].vl = a[l];
}else
{
int m = (l + r)/2;
build(id*2, l, m);
build(id*2+1, m+1, r);
Tree[id].vl = max(Tree[id*2].vl, Tree[id*2+1].vl);
}
}
void down(int id)
{
Node &P = Tree[id], &L = Tree[id*2], &R = Tree[id*2+1];
if (P.lz)
{
L.vl += P.lz;
R.vl += P.lz;
L.lz += P.lz;
R.lz += P.lz;
P.lz = 0;
}
}
void update(int id, int l, int r, int u, int v, ll vl)
{
if (l > v || r < u) return;
if (l >= u && r <= v)
{
Tree[id].vl += vl;
Tree[id].lz += vl;
return;
}
down(id);
int m = (l + r)/2;
update(id*2, l, m, u, v, vl);
update(id*2+1, m+1, r, u, v, vl);
Tree[id].vl = max(Tree[id*2].vl, Tree[id*2+1].vl);
}
ll query(int id, int l, int r, int u, int v)
{
if (l > v || r < u) return INT_MIN;
if (l >= u && r <= v) return Tree[id].vl;
down(id);
int m = (l+r)/2;
int L = query(id*2, l, m, u, v);
int R = query(id*2+1, m+1, r, u, v);
return max(L, R);
}
} S;
/*
/* DSU
struct DSU
{
vector<ll> lab;
int n;
DSU(int _n = 0)
{
n = _n;
lab.resize(n + 1);
fill(lab.begin(), lab.end(), -1);
}
int Find(int u)
{
return lab[u] < 0 ? u : lab[u] = Find(lab[u]);
}
ll Union(int u, int v)
{
u = Find(u);
v = Find(v);
if (u == v) return 0;
ll res = 1ll * lab[u] * lab[v];
if (lab[u] > lab[v]) swap(u, v);
lab[u] += lab[v];
lab[v] = u;
return res;
}
} D;
*/
/* NENSO
void nenso()
{
sort(vt.begin(), vt.end());
vt.resize(unique(vt.begin(), vt.end()) - vt.begin());
fu(i,1,n) a[i] = lower_bound(vt.begin(), vt.end(), a[i]) - vt.begin() + 1;
fu(i,1,q)
{
st[i].x = lower_bound(vt.begin(), vt.end(), st[i].x) - vt.begin() + 1;
if (st[i].tp == '?') st[i].k = lower_bound(vt.begin(), vt.end(), st[i].k) - vt.begin() + 1;
}
}
*/
/* Kruskal
bool cmp(Edge a, Edge b)
{
return a.c < b.c;
}
vector<Edge> mst;
void kruskal()
{
sort(st + 1, st + m +1, cmp);
ll d = 0;
for (int i = 1; i <= m; i++)
{
if (mst.size() == n - 1) break;
if (Union(st[i].u, st[i].v))
{
mst.push_back(st[i]);
d += st[i].c;
}
}
}
*/
/* SPARSE TABLE
int log2_floor(int n) { return 31 - __builtin_clz(n); }
ll query_rmq(int l, int r)
{
int i = log2_floor(r-l+1);
return min(table[i][l], table[i][r - MASK(i) + 1]);
}
void pre
{
fu(i,1,n) table[0][i] = a[i];
fu(j,1,Log)
{
for (int i = 1; i + MASK(j) - 1 <= n; i++)
{
table[j][i] = min(table[j-1][i], table[j-1][i + MASK(j - 1)]);//rmq hay rsq thi thay doi min hoac s
}
}
}
*/
/* KIEM TRA CHU TRINH
1. DO THI VO HUONG DUNG DSU
2. DO THI CO HUONG
bool dfs(int u)
{
col[u] = 1;
for (int v : adj[u])
{
if (col[v] == 0)
{
par[v] = u;
if (dfs(v)) return true;
}else if (col[v] == 1) return true;
}
col[u] = 2;
return false;
}
*/
/*
LCA
void dfs(int u, int p)
{
for (int v : adj[u]) if (v != p)
{
high[v] = high[u] + 1;
par[v][0] = u;
dfs(v, u);
}
}
void pre()
{
dfs(1, -1);
for (int j = 1; j <= Log; j++)
{
for (int i = 1; i <= n; i++)
{
par[i][j] = par[par[i][j-1]][j-1];
}
}
high[0] = -1;
}
int lca(int u, int v)
{
if (high[v] > high[u]) return lca(v, u);
fd(i, Log, 0)
{
if(high[par[u][i]] >= high[v])
u = par[u][i];
}
if (u == v) return u;
fd(i, Log, 0)
{
if (par[u][i] != par[v][i])
{
u = par[u][i];
v = par[v][i];
}
}
return par[u][0];
}
*/
/* ERAS DOAN
void eras_doan()
{
fu(i,2,(int)1e6)
{
ll j = (l + i - 1) /i *i;
for (;j<=r; j+=i) if (j != i)
d[j-l] = 1
}
for (int i = 0; i < r-l; i++) if (d[i]==0) cout<<i+l<<sp;
}
*/
/* LUONG CUC DAI
struct edge
{
int x, y, cap, flow;
};
struct Flow
{
int n, S, T;
vector < vector <int> > a;
vector <int> cur, d;
vector <edge> e;
Flow() {}
Flow(int _n, int _S, int _T)
{
n = _n; S = _S; T = _T;
a = vector < vector <int> >(n + 1);
cur = vector <int>(n + 1);
d = vector <int>(n + 1);
}
void addEdge(int x, int y, int _cap)
{
edge e1 = {x, y, _cap, 0};
edge e2 = {y, x, 0, 0};
a[x].push_back(e.size()); e.push_back(e1);
a[y].push_back(e.size()); e.push_back(e2);
}
int bfs()
{
queue<int> q;
for (int i = 1; i <= n; i++) d[i] = -1;
q.push(S); d[S] = 0;
while (!q.empty() && d[T] < 0)
{
int x = q.front(); q.pop();
for (int i = 0; i < (int)a[x].size(); i++)
{
int id = a[x][i], y = e[id].y;
if (d[y] < 0 && e[id].flow < e[id].cap)
q.push(y), d[y] = d[x] + 1;
}
}
return d[T] >= 0;
}
int dfs(int x, int val)
{
if (!val) return 0;
if (x == T) return val;
for (; cur[x] < (int)a[x].size(); cur[x]++)
{
int id = a[x][cur[x]], y = e[id].y;
if (d[y] != d[x] + 1) continue;
int pushed = dfs(y, min(val, e[id].cap - e[id].flow));
if (pushed)
{
e[id].flow += pushed;
e[id ^ 1].flow -= pushed;
return pushed;
}
}
return 0;
}
int maxFlow()
{
int res = 0;
while (bfs())
{
for (int i = 1; i <= n; i++) cur[i] = 0;
while (1)
{
int val = dfs(S, oo);
if (!val) break;
res += val;
}
}
return res;
}
};
*/
/* Matrix Multiplication
const int MATRIX_SIZE = 20;
struct Matrix {
int m, n;
long long d[MATRIX_SIZE][MATRIX_SIZE];
Matrix(int _m = 0, int _n = 0) {
m = _m; n = _n;
memset(d, 0, sizeof d);
}
Matrix operator + (const Matrix &a) const {
Matrix res(m, n);
for (int i = 0; i < m; i++) for (int j = 0; j < n; j++) {
res.d[i][j] = d[i][j] + a.d[i][j];
if (res.d[i][j] >= MOD) res.d[i][j] -= MOD;
}
return res;
}
Matrix operator * (const Matrix &a) const {
int x = m, y = n, z = a.n;
Matrix res(x, z);
for (int i = 0; i < x; i++) for (int j = 0; j < y; j++)
for (int k = 0; k < z; k++) {
res.d[i][k] += 1LL * d[i][j] * a.d[j][k];
if (res.d[i][k] >= 1LL * MOD * MOD) res.d[i][k] -= 1LL * MOD * MOD;
}
for (int i = 0; i < x; i++) for (int k = 0; k < z; k++) res.d[i][k] %= MOD;
return res;
}
Matrix operator ^ (long long k) const {
Matrix res(n, n);
for (int i = 0; i < n; i++) res.d[i][i] = 1;
Matrix mul = *this;
while (k > 0) {
if (k & 1) res = res * mul;
mul = mul * mul;
k >>= 1;
}
return res;
}
long long* operator[] (int i) {
return d[i];
}
const long long* operator[] (int i) const {
return d[i];
}
};
*/
/* CAP GHEP CUC DAI KHONG TRONG SO
struct matcher {
const int oo = 100000000;
int m, n;
vector<int> mx, my, dist;
vector<vector<int>> ke;
int matched;
matcher(int m, int n):
m(m), n(n),
mx(m+1, 0), my(n+1, 0), dist(m+1),
ke(m+1),
matched(0) {}
void add_edge(int u, int v) {
ke[u].push_back(v);
}
bool bfs() {
queue<int> Q;
for (int u=1; u<=m; u++) {
if (!mx[u]) {
dist[u] = 0;
Q.push(u);
} else {
dist[u] = oo;
}
}
bool found = false;
while (!Q.empty()) {
int u = Q.front(); Q.pop();
for (int v: ke[u]) {
if (!my[v]) {
found = true;
} else if (dist[my[v]] == oo) {
dist[my[v]] = dist[u] + 1;
Q.push(my[v]);
}
}
}
return found;
}
bool dfs(int u) {
if (dist[u] == oo) return false;
for (int v: ke[u]) {
if (!my[v] || (dist[my[v]]==dist[u]+1 && dfs(my[v]))) {
mx[u] = v;
my[v] = u;
return true;
}
}
return false;
}
void match() {
while(bfs()) {
for (int u=1; u<=m; u++) if (!mx[u]) matched += dfs(u);
}
}
};
int get()
{
matcher z(n, n);
fu(i,1,m)
{
int u, v; cin>>u>>v;
z.add_edge(u, v);
}
z.match();
return z.matched;
}
*/
signed main()
{
}
#include <bits/stdc++.h>

using namespace std;
/* Merge 2 vector thanh 1
 merge(Tree[2 * id].begin(), Tree[2 * id].end(),
              Tree[2 * id + 1].begin(), Tree[2 * id + 1].end(),
              back_inserter(Tree[id]));
*/

/*legendry
int legendry(int n, int p)
{
    int ans = 0, x = 1;
    while (x * p <= n)
    {
        x *= p;
        ans += n/x;
    }
    return ans;
}
*/

/* Phi ham euler
int Phi(int x)
{
    int res = 0;
    for (int i = 2; i <= sqrt(x); i++)
    {
        if (x % i == 0)
        {
            res -= res / i;
            while (x % i == 0)
            {
                x /= i;
            }
        }
    }
    if (x > 1) res -= res / x;
    return res;
}

int phi[N];

void sang(int x)
{
    fu(i, 1, x) phi[i] = i;

    fu(i, 2, x)
    {
        if (phi[i] == i)
        {
            for (int j = i; j <= x; j += i)
            {
                phi[j] -= phi[j] / i;
            }
        }
    }
}
*/

/* To Hop
const int MAX = 2e5 + 1;

int powmod(int a, int b)
{
    if (b == 0) return 1;
    else if (b == 1) return a % MOD;
    int vl = powmod(a, b/2);
    if (b % 2 == 0) return vl * vl % MOD;
    return 1ll * (vl * vl % MOD) * (a % MOD) % MOD;
}

void preComb()
{
    frac[0] = 1;
    fu(i,1,MAX) frac[i] = 1LL * frac[i - 1] * i % MOD;
    finv[MAX] = powmod(frac[MAX], MOD - 2);
    fd(i,MAX,1) finv[i - 1] = 1LL * finv[i] * i % MOD;
}

int Comb(int k, int n)
{
    return k > n ? 0 : 1LL * frac[n] * finv[k] % MOD * finv[n - k] % MOD;
}
*/

/* Fenwick 2d
struct Fenwick2D
{
    vector<vector<int>> Tree;
    int m, n;
    Fenwick2D(int _m = 0, int _n = 0)
    {
        m = _m;
        n = _n;
        Tree.resize(m + 1);
        fu(i,0,m)
        {
            Tree[i].resize(n + 1);
            fill(Tree[i].begin(), Tree[i].end(), 0);
        }
    }
    void update(int x, int y, int vl)
    {
        for(int i = x; i <= m; i += i&-i)
        {
            for(int j = y; j <= n; j += j&-j)
            {
                Tree[i][j] += vl;
            }
        }
    }
    int get(int x, int y)
    {
        int res = 0;
        for(int i = x; i > 0; i -= i&-i)
        {
            for(int j = y; j > 0; j -= j&-j)
            {
                res += Tree[i][j];
            }
        }
        return res;
    }
} F2D;
*/
/* HLD
 void dfs(int u, int p)
 {
     child[u] = 1;
     for (int v : adj[u]) if (v != p)
     {
         par[v] = u;
         depth[v] = depth[u] + 1;
         dfs(v, u);
         child[u] += child[v];
     }
 }

 int lca(int u, int v)
 {
    while(ChainId[u] != ChainId[v])
    {
        if(ChainId[u] > ChainId[v])
        {
            u = par[head[ChainId[u]]];
        }
        else
        {
            v = par[head[ChainId[v]]];
        }
    }
    if(depth[u] < depth[v]) return u;
    return v;
}

void hld(int u, int p)
 {
     if (!head[CurChain]) head[CurChain] = u;
     ChainId[u] = CurChain;
     Pos[u] = ++CurPos;
     Arr[CurPos] = v[u];
     int MaxNode = 0;
     for(int v : adj[u]) if (v != p)
     {
         if (child[v] > child[MaxNode]) MaxNode = v;
     }
     if (MaxNode) hld(MaxNode, u);
     for(int v : adj[u]) if (v != p && v != MaxNode)
     {
         CurChain++;
         hld(v, u);
     }
 }

 int Query(int u, int v)
{
    int Lca = lca(u, v);
    int ans = LLONG_MIN;
    while (ChainId[u] != ChainId[Lca])
    {
        maximize(ans, S.query(1,1,CurPos,Pos[head[ChainId[u]]], Pos[u]));
        u = par[head[ChainId[u]]];
    }
    while (ChainId[v] != ChainId[Lca])
    {
        maximize(ans, S.query(1,1,CurPos,Pos[head[ChainId[v]]], Pos[v]));
        v = par[head[ChainId[v]]];
    }
    if (depth[u] < depth[v])
    {
        maximize(ans, S.query(1,1,CurPos,Pos[u],Pos[v]));
    }else maximize(ans, S.query(1,1,CurPos,Pos[v],Pos[u]));
    return ans;
}
*/

/*
Convex Hull Trick Min
int pointer;
vector<ll> M;
vector<ll> B;

bool bad(int l1,int l2,int l3)
{
	return (B[l3] - B[l1]) * (M[l1] - M[l2]) < (B[l2] - B[l1]) * (M[l1] - M[l3]);
}

void add(ll m,ll b)
{
	M.push_back(m);
	B.push_back(b);
	while (M.size() >= 3 && bad(M.size() - 3, M.size() - 2, M.size() - 1))
	{
		M.erase(M.end()-2);
		B.erase(B.end()-2);
	}
}

ll query(ll x)
{
	if (pointer >= M.size())
        pointer = M.size() - 1;
	while (pointer < M.size() - 1 && M[pointer+1] * x + B[pointer+1] < M[pointer] * x + B[pointer])
		pointer++;
	return M[pointer] * x + B[pointer];
}
*/

/* TRIE
struct Trie
{
    struct Node
    {
        bool isEnd;
        Node *child[26];
        Node()
        {
            fu(i,0,25) child[i] = nullptr;
            isEnd = 0;
        }
    };
    Node *root = new Node();
    void add(string str)
    {
        Node *x = root;
        fu(i,0,str.size()-1)
        {
            int c = str[i] - 'a';
            if (x->child[c] == nullptr) x->child[c] = new Node();
            x = x->child[c];
        }
        x->isEnd = 1;
    }
    bool query(string str)
    {
        Node *x = root;
        fu(i,0,str.size()-1)
        {
            int c = str[i] - 'a';
            if (x->child[c] == nullptr) return false;
            else x = x->child[c];
        }
        return (x->isEnd == 1);
    }
} T;
*/

/* KMP
int kmp[N], match[N];

void cre_kmp()
{
    int k = kmp[1] = 0;
    fu(i,2,m)
    {
        while (k > 0 && B[i] != B[k+1]) k = kmp[k];
        kmp[i] = B[i] == B[k+1] ? ++k : 0;
    }
}

void cre_match()
{
    int k = 0;
    fu(i,1,n)
    {
        while(k > 0 && A[i] != B[k+1]) k = kmp[k];
        match[i] = A[i] == B[k+1] ? ++k : 0;
        if (match[i] == m) cout<<i - m + 1<<sp;
    }
}
*/

/* CHIA CAN
   fu(i,1,q)
    {
        int t; cin>>t;
        if (t == 1)
        {
            int u, v; cin>>u>>v;
            auto it = blck[u/sq].lower_bound(a[u]);
            blck[u/sq].erase(it);
            a[u] = v;
            blck[u/sq].insert(a[u]);
        }
        else
        {
            int L, R, k; cin>>L>>R>>k;
            int res = INT_MAX;
            int blockL = (L - 1) / sq + 1;
            int blockR = R / sq - 1;

            fu(i,blockL,blockR)
            {
                auto it = blck[i].lower_bound(k);
                if (it != blck[i].end()) minimize(res, *it);
            }

            if (L/sq != R/sq)
            {
                fu(i,L,blockL*sq-1) if (a[i] >= k) minimize(res, a[i]);
                fu(i,(blockR+1)*sq,R) if (a[i] >= k) minimize(res, a[i]);
            }
            else fu(i,L,R) if (a[i] >= k) minimize(res, a[i]);
            cout<<(res == INT_MAX ? -1 : res)<<el;
        }
    }
    */

/* DIJSKTRA
void dijkstra(int st)
{
    d[st] = 0;
    priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> q;
    q.push({0,st});
    while (!q.empty())
    {
        pair<l, int> tmp = q.top();
        q.pop();
        int u = tmp.second;
        int w = tmp.first;
        if (w > d[u]) continue;
        for (auto it : adj[u])
        {
            int v = it.first;
            int c = it.second;
            if (maximize(d[v], w + c))
            {
                q.push({d[v], v});
            }
        }
    }
}

/* FENWICK TREE
struct Fenwick
{
    vector<pair<ll, int>> Tree;
    int n;
    Fenwick(int _n = 0)
    {
        n = _n;
        Tree.resize(n+1);
    }
    void update(ll x, ll vl)
    {
        for(;x<=n;x+=x&-x)
        {
            Tree[x].first+=vl;
            Tree[x].second++;
        }
    }
    pair<ll,int> get(ll x)
    {
        pair<ll, int> tmp;
        for(;x;x-=x&-x)
        {
            tmp.first += Tree[x].first;
            tmp.second += Tree[x].second;
        }
        return tmp;
    }
    pair<ll,int> query(int l, int r)
    {
        if (l == 0) return get(r);
        return {get(r).first - get(l-1).first, get(r).se - get(l-1).se};
    }
} F;

/* SEGMENT TREE
struct Segment
{
    struct Node
    {
        ll vl, lz;
        Node(ll _vl = 0, ll _lz = 0)
        {
            vl = _vl;
            lz = _lz;
        }
    };
    vector<Node> Tree;
    int n;
    Segment(int _n = 0)
    {
        n = _n;
        Tree.resize(4*n+1);
    }
    void build(int id, int l, int r)
    {
        if (l == r)
        {
            Tree[id].vl = a[l];
        }else
        {
            int m = (l + r)/2;
            build(id*2, l, m);
            build(id*2+1, m+1, r);
            Tree[id].vl = max(Tree[id*2].vl, Tree[id*2+1].vl);
        }
    }
    void down(int id)
    {
        Node &P = Tree[id], &L = Tree[id*2], &R = Tree[id*2+1];
        if (P.lz)
        {
            L.vl += P.lz;
            R.vl += P.lz;
            L.lz += P.lz;
            R.lz += P.lz;
            P.lz = 0;
        }
    }
    void update(int id, int l, int r, int u, int v, ll vl)
    {
        if (l > v || r < u) return;
        if (l >= u && r <= v)
        {
            Tree[id].vl += vl;
            Tree[id].lz += vl;
            return;
        }
        down(id);
        int m = (l + r)/2;
        update(id*2, l, m, u, v, vl);
        update(id*2+1, m+1, r, u, v, vl);
        Tree[id].vl = max(Tree[id*2].vl, Tree[id*2+1].vl);
    }
    ll query(int id, int l, int r, int u, int v)
    {
        if (l > v || r < u) return INT_MIN;
        if (l >= u && r <= v) return Tree[id].vl;
        down(id);
        int m = (l+r)/2;
        int L = query(id*2, l, m, u, v);
        int R = query(id*2+1, m+1, r, u, v);
        return max(L, R);
    }
} S;
/*

/* DSU
struct DSU
{
    vector<ll> lab;
    int n;
    DSU(int _n = 0)
    {
        n = _n;
        lab.resize(n + 1);
        fill(lab.begin(), lab.end(), -1);
    }
    int Find(int u)
    {
        return lab[u] < 0 ? u : lab[u] = Find(lab[u]);
    }
    ll Union(int u, int v)
    {
        u = Find(u);
        v = Find(v);
        if (u == v) return 0;
        ll res = 1ll * lab[u] * lab[v];
        if (lab[u] > lab[v]) swap(u, v);
        lab[u] += lab[v];
        lab[v] = u;
        return res;
    }
} D;
*/

/* NENSO
void nenso()
{
    sort(vt.begin(), vt.end());
    vt.resize(unique(vt.begin(), vt.end()) - vt.begin());
    fu(i,1,n) a[i] = lower_bound(vt.begin(), vt.end(), a[i]) - vt.begin() + 1;
    fu(i,1,q)
    {
        st[i].x = lower_bound(vt.begin(), vt.end(), st[i].x) - vt.begin() + 1;
        if (st[i].tp == '?') st[i].k = lower_bound(vt.begin(), vt.end(), st[i].k) - vt.begin() + 1;
    }
}
*/

/* Kruskal
bool cmp(Edge a, Edge b)
{
    return a.c < b.c;
}

vector<Edge> mst;

void kruskal()
{
    sort(st + 1, st + m +1, cmp);
    ll d = 0;
    for (int i = 1; i <= m; i++)
    {
        if (mst.size() == n - 1) break;
        if (Union(st[i].u, st[i].v))
        {
            mst.push_back(st[i]);
            d += st[i].c;
        }
    }
}
*/

/* SPARSE TABLE

int log2_floor(int n) { return 31 - __builtin_clz(n); }


ll query_rmq(int l, int r)
{
    int i = log2_floor(r-l+1);
    return min(table[i][l], table[i][r - MASK(i) + 1]);
}

void pre
{
    fu(i,1,n) table[0][i] = a[i];

    fu(j,1,Log)
    {
        for (int i = 1; i + MASK(j) - 1 <= n; i++)
        {
            table[j][i] = min(table[j-1][i], table[j-1][i + MASK(j - 1)]);//rmq hay rsq thi thay doi min hoac s
        }
    }
}
*/

/* KIEM TRA CHU TRINH
1. DO THI VO HUONG DUNG DSU
2. DO THI CO HUONG
bool dfs(int u)
{
    col[u] = 1;
    for (int v : adj[u])
    {
        if (col[v] == 0)
        {
            par[v] = u;
            if (dfs(v)) return true;
        }else if (col[v] == 1) return true;
    }
    col[u] = 2;
    return false;
}
*/

/*
LCA

void dfs(int u, int p)
{
    for (int v : adj[u]) if (v != p)
    {
        high[v] = high[u] + 1;
        par[v][0] = u;
        dfs(v, u);
    }
}

void pre()
{
    dfs(1, -1);

    for (int j = 1; j <= Log; j++)
    {
        for (int i = 1; i <= n; i++)
        {
            par[i][j] = par[par[i][j-1]][j-1];
        }
    }
    high[0] = -1;
}

int lca(int u, int v)
{
    if (high[v] > high[u]) return lca(v, u);

    fd(i, Log, 0)
    {
        if(high[par[u][i]] >= high[v])
            u = par[u][i];
    }

    if (u == v) return u;

    fd(i, Log, 0)
    {
        if (par[u][i] != par[v][i])
        {
            u = par[u][i];
            v = par[v][i];
        }
    }
    return par[u][0];
}
*/

/* ERAS DOAN
void eras_doan()
{
    fu(i,2,(int)1e6)
    {
        ll j = (l + i - 1) /i *i;
        for (;j<=r; j+=i) if (j != i)
            d[j-l] = 1
    }
    for (int i = 0; i < r-l; i++) if (d[i]==0) cout<<i+l<<sp;
}
*/

/* LUONG CUC DAI
struct edge
{
    int x, y, cap, flow;
};

struct Flow
{
    int n, S, T;
    vector < vector <int> > a;
    vector <int> cur, d;
    vector <edge> e;

    Flow() {}
    Flow(int _n, int _S, int _T)
    {
        n = _n; S = _S; T = _T;
        a = vector < vector <int> >(n + 1);
        cur = vector <int>(n + 1);
        d = vector <int>(n + 1);
    }

    void addEdge(int x, int y, int _cap)
    {
        edge e1 = {x, y, _cap, 0};
        edge e2 = {y, x, 0, 0};
        a[x].push_back(e.size()); e.push_back(e1);
        a[y].push_back(e.size()); e.push_back(e2);
    }

    int bfs()
    {
        queue<int> q;
        for (int i = 1; i <= n; i++) d[i] = -1;
        q.push(S); d[S] = 0;
        while (!q.empty() && d[T] < 0)
        {
            int x = q.front(); q.pop();
            for (int i = 0; i < (int)a[x].size(); i++)
            {
                int id = a[x][i], y = e[id].y;
                if (d[y] < 0 && e[id].flow < e[id].cap)
                    q.push(y), d[y] = d[x] + 1;
            }
        }
        return d[T] >= 0;
    }

    int dfs(int x, int val)
    {
        if (!val) return 0;
        if (x == T) return val;
        for (; cur[x] < (int)a[x].size(); cur[x]++)
        {
            int id = a[x][cur[x]], y = e[id].y;
            if (d[y] != d[x] + 1) continue;
            int pushed = dfs(y, min(val, e[id].cap - e[id].flow));
            if (pushed)
            {
                e[id].flow += pushed;
                e[id ^ 1].flow -= pushed;
                return pushed;
            }
        }
        return 0;
    }

    int maxFlow()
    {
        int res = 0;
        while (bfs())
        {
            for (int i = 1; i <= n; i++) cur[i] = 0;
            while (1)
            {
                int val = dfs(S, oo);
                if (!val) break;
                res += val;
            }
        }
        return res;
    }
};
*/

/* Matrix Multiplication
const int MATRIX_SIZE = 20;

struct Matrix {
    int m, n;
    long long d[MATRIX_SIZE][MATRIX_SIZE];

    Matrix(int _m = 0, int _n = 0) {
        m = _m; n = _n;
        memset(d, 0, sizeof d);
    }

    Matrix operator + (const Matrix &a) const {
        Matrix res(m, n);
        for (int i = 0; i < m; i++) for (int j = 0; j < n; j++) {
            res.d[i][j] = d[i][j] + a.d[i][j];
            if (res.d[i][j] >= MOD) res.d[i][j] -= MOD;
        }
        return res;
    }

    Matrix operator * (const Matrix &a) const {
        int x = m, y = n, z = a.n;
        Matrix res(x, z);
        for (int i = 0; i < x; i++) for (int j = 0; j < y; j++)
		for (int k = 0; k < z; k++) {
            	res.d[i][k] += 1LL * d[i][j] * a.d[j][k];
            	if (res.d[i][k] >= 1LL * MOD * MOD) res.d[i][k] -= 1LL * MOD * MOD;
        	}
        for (int i = 0; i < x; i++) for (int k = 0; k < z; k++) res.d[i][k] %= MOD;

        return res;
    }

    Matrix operator ^ (long long k) const {
        Matrix res(n, n);
        for (int i = 0; i < n; i++) res.d[i][i] = 1;
        Matrix mul = *this;
        while (k > 0) {
            if (k & 1) res = res * mul;
            mul = mul * mul;
            k >>= 1;
        }
        return res;
    }

    long long* operator[] (int i) {
        return d[i];
    }

    const long long* operator[] (int i) const {
        return d[i];
    }
};
*/

/* CAP GHEP CUC DAI KHONG TRONG SO
struct matcher {
    const int oo = 100000000;
    int m, n;
    vector<int> mx, my, dist;
    vector<vector<int>> ke;
    int matched;

    matcher(int m, int n):
        m(m), n(n),
        mx(m+1, 0), my(n+1, 0), dist(m+1),
        ke(m+1),
        matched(0) {}

    void add_edge(int u, int v) {
        ke[u].push_back(v);
    }

    bool bfs() {
        queue<int> Q;
        for (int u=1; u<=m; u++) {
            if (!mx[u]) {
                dist[u] = 0;
                Q.push(u);
            } else {
                dist[u] = oo;
            }
        }

        bool found = false;
        while (!Q.empty()) {
            int u = Q.front(); Q.pop();
            for (int v: ke[u]) {
                if (!my[v]) {
                    found = true;
                } else if (dist[my[v]] == oo) {
                    dist[my[v]] = dist[u] + 1;
                    Q.push(my[v]);
                }
            }
        }

        return found;
    }

    bool dfs(int u) {
        if (dist[u] == oo) return false;
        for (int v: ke[u]) {
            if (!my[v] || (dist[my[v]]==dist[u]+1 && dfs(my[v]))) {
                mx[u] = v;
                my[v] = u;
                return true;
            }
        }
        return false;
    }

    void match() {
        while(bfs()) {
            for (int u=1; u<=m; u++) if (!mx[u]) matched += dfs(u);
        }
    }
};

int get()
{
    matcher z(n, n);
    fu(i,1,m)
    {
        int u, v; cin>>u>>v;
        z.add_edge(u, v);
    }
    z.match();
    return z.matched;
}
*/

signed main()
{

}
