#pragma GCC optimize("Ofast,unroll-loops")
#pragma GCC target("avx2")
#include "joitour.h"
#include <bits/stdc++.h>
using namespace std;
using ll = int; using pii = pair<ll,ll>;
const ll Nm = 2e5+5;

ll N;
long long ans = 0;
vector<int> F,U,V;
vector<pii> locs[Nm]; //{index of subtree, index in subtree}
ll rlbl[Nm];
//vector<ll> hld;

const ll Sm = 4194304; const ll E = 22;

//long long sts0[2*Sm]; //already pushed sum s0
int na0[2*Sm];  //number active in 0
int pd0[2*Sm]; //number to push down
//long long sts2[2*Sm];
int na2[2*Sm];
int pd2[2*Sm];
ll allc = 0; //allocator for memory

ll v2(ll x) {
    return __builtin_ctz(x);
}

inline void pdn0(ll p) { //push down at position p
    //return;
    //sts0[p]+=stna0[p]*pd0[p];
    pd0[2*p]+=pd0[p];
    pd0[2*p+1]+=pd0[p];
    pd0[p]=0;
}

inline void pdn2(ll p) { //push down at position p
    //return;
    //sts2[p]+=stna2[p]*pd2[p];
    pd2[2*p]+=pd2[p];
    pd2[2*p+1]+=pd2[p];
    pd2[p]=0;
}

ll wrt0(ll x, ll v) { //v is the DELTA
    //return 0;
    for (ll e=16;e>0;e--) {
        pdn0((x>>e)+(1LL<<(E-e)));
    }
    //sts0[x+Sm] += v*pd0[x+Sm];
    na0[x+Sm] += v;
    for (ll e=1;e<=16;e++) {
        ll p = ((x>>e)+(1LL<<(E-e)));
        //sts0[p] += v*pd0[x+Sm];
        na0[p] += v;
    }
    return v*pd0[x+Sm];
}

ll wrt2(ll x, ll v) {
    //return 0;
    for (ll e=16;e>0;e--) {
        pdn2((x>>e)+(1LL<<(E-e)));
    }
   // sts2[x+Sm] += v*pd2[x+Sm];
    na2[x+Sm] += v;
    for (ll e=1;e<=16;e++) {
        ll p = ((x>>e)+(1<<(E-e)));
        //sts2[p] += v*pd2[x+Sm];
        na2[p] += v;
    }
    return v*pd2[x+Sm];
}

pii wrtI(ll x, ll y, ll v) { //return {n21, n01} updates
    //cout << "write 1 to range "<<x<<","<<y<<"\n";
    //return {0,0};
    if (x>y) {
        return {0,0};
    }
    ll vx = v2(x); ll vy = v2(y+1);
    if (vx<vy) {
        ll p = (x>>vx)+(1<<(E-vx));
        pii p1 = {v*na0[p],v*na2[p]};
        pd0[p]+=v; pd2[p]+=v;
        pii p2 = wrtI(x+(1<<vx),y,v);
        return {p1.first+p2.first,p1.second+p2.second};
    } else {
        ll p = (y>>vy)+(1<<(E-vy));
        pii p1 = {v*na0[p],v*na2[p]};
        pd0[p]+=v; pd2[p]+=v;
        pii p2 = wrtI(x,y-(1<<vy),v);
        return {p1.first+p2.first,p1.second+p2.second};
    }
}

struct cst { //cdt subtree
    ll M;
    long long n0,n2,n21,n01;
    vector<ll> Fn;
    ll r;
    vector<vector<ll>> fadj;
    vector<ll> radj;
    vector<int> tsz; //subtree size
    vector<int> sti; //segtree index
   // vector<long long> v0,v2,v21,v01;
    /*void lft(ll x) {
        v0[x]=(Fn[x]==0);
        v2[x]=(Fn[x]==2);
        v21[x]=0;
        v01[x]=0;
        for (ll y: fadj[x]) {
            lft(y);
            v0[x]+=v0[y];
            v2[x]+=v2[y];
            v01[x]+=v01[y];
            v21[x]+=v21[y];
        }
        if (Fn[x]==1) {
            v01[x]+=v0[x];
            v21[x]+=v2[x];
        }
    }
    void calc() {
        vector<long long> emp(M,0);
        v0=emp; v2=emp; v21=emp; v01=emp;
        lft(r);
        n0=v0[r]; n2=v2[r]; n21=v21[r]; n01=v01[r];
        v0.clear(); v2.clear(); v21.clear(); v01.clear();
    }*/
    cst(ll r0, ll M0, vector<vector<ll>> adj,vector<ll> f0) {
        n0=0; n2=0; n21=0; n01=0;
        r=r0; M=M0;
        Fn=f0;
        vector<bool> found;
        for (ll m=0;m<M;m++) {
            tsz.push_back(0);
            sti.push_back(0);
            radj.push_back(-1);
            found.push_back(0);
            fadj.push_back((vector<ll>){});
        }
        // queue<ll> q;
        // q.push(r);
        // while (!q.empty()) {
        //     ll x = q.front(); q.pop();
        //     found[x]=1;
        //     for (ll y: adj[x]) {
        //         if (!found[y]) {
        //             radj[y]=x;
        //             q.push(y);
        //             fadj[x].push_back(y);
        //         }
        //     }
        // }
        stack<pii> q0;
        q0.push({r,0});
        while (!q0.empty()) {
            pii p0 = q0.top(); q0.pop();
            ll x = p0.first; ll t = p0.second;
            if (t==0) {
                found[x]=1;
                q0.push({x,1});
                for (ll y: adj[x]) {
                    if (!found[y]) {
                        radj[y]=x;
                        q0.push({y,0});
                        fadj[x].push_back(y);
                    }
                }
            } else {
                tsz[x]=1;
               // cout << "x="<<x<<", Fn[x]="<<Fn[x]<<"\n";
                for (ll y: adj[x]) {
                   // cout << "y in fadj="<<y<<"\n";
                    if (radj[y]==x) {
                        //cout << "f1\n";
                        tsz[x]+=tsz[y];
                    }
                }
                //cout << "tsz[x]="<<tsz[x]<<"\n";
                sti[x]=allc;
                if (f0[x]==0) {
                    n0++;
                    n01 += wrt0(allc,1); //v is the DELTA
                } else if (f0[x]==2) {
                    n2++;
                    n21 += wrt2(allc,1);
                } else {
                    pii p1mod = wrtI(allc-tsz[x]+1,allc,1);
                    n01 = p1mod.first+n01;
                    n21 = p1mod.second+n21;
                }
                allc++;
            }
        }
        //cout << "n0,n2,n01,n21="<<n0<<","<<n2<<","<<n01<<","<<n21<<"\n";
        //calc();
    }
    /*void upd(ll x, ll v) {
        Fn[x]=v;
        calc();
    }*/
    void upd(ll x, ll v) {
        if (Fn[x]==0) {
            n0--;
            n01 += wrt0(sti[x],-1);
        } else if (Fn[x]==2) {
            n2--;
            n21 += wrt2(sti[x],-1);
        } else {
            pii p1mod = wrtI(sti[x]-tsz[x]+1,sti[x],-1);
            n01 = p1mod.first+n01;
            n21 = p1mod.second+n21;
        }
        Fn[x]=v;
        if (Fn[x]==0) {
            n0++;
            n01 += wrt0(sti[x],1);
        } else if (Fn[x]==2) {
            n2++;
            n21 += wrt2(sti[x],1);
        } else {
            pii p1mod = wrtI(sti[x]-tsz[x]+1,sti[x],1);
            n01 = p1mod.first+n01;
            n21 = p1mod.second+n21;
        }
       // cout << "n0,n2,n01,n21="<<n0<<","<<n2<<","<<n01<<","<<n21<<"\n";
    }
}; 

struct cdt { //centroid decomp tree
    ll M; //size
    vector<vector<ll>> fadj;
    vector<ll> Fn; //new F
    vector<pii> strl; //subtree locations: {index of st, index in st}
    vector<cst*> v1;
    long long s21=0, s01=0, s0=0, s2=0, s210=0, s012=0, s02=0;
    cdt(ll M1, vector<vector<ll>> fadj1, vector<ll> Fn1) { //fadj is really just adj oops
        M=M1; fadj=fadj1; Fn=Fn1;
        for (ll m=0;m<M;m++) {
            strl.push_back((pii){0,0});
        }
        ll rcnt = 0;
        for (ll x: fadj[0]) {
            //unordered_map<ll,ll> rlbl; //relabel
            vector<vector<ll>> nadj;
            vector<ll> fnew;
            ll Mn = 0;
            queue<pii> q0;
            q0.push({x,-1});
            //cout << "x="<<x<<"\n";
            while (!q0.empty()) {
                pii p0 = q0.front(); q0.pop();
                ll z = p0.first; ll pz = p0.second;
                if (z==0) {
                    continue;
                }
                //if (rlbl.find(z)==rlbl.end()) {
                    rlbl[z]=Mn++;
                    //cout << "defining z="<<z<<" as "<<rlbl[z]<<"\n";
                    nadj.push_back((vector<ll>){});
                    fnew.push_back(Fn[z]);
                    strl[z]={rcnt,rlbl[z]};
                    //cout << "relabel: z="<<z<<"->"<<rlbl[z]<<"\n";
                    //locs[z].push_back({dind,rlbl[z]});
               // }
                if (pz != -1) {
                    //cout << "z,pz="<<z<<","<<pz<<"\n";
                    nadj[rlbl[z]].push_back(rlbl[pz]);
                    nadj[rlbl[pz]].push_back(rlbl[z]);
                }
                for (ll nz: fadj[z]) {
                    if (nz != pz && nz != 0) {
                        q0.push({nz,z});
                    }
                }
            }
            v1.push_back(new cst(0LL,Mn,nadj,fnew));
            rcnt++;
        }
        for (ll r=0;r<rcnt;r++) {
            s21 += (v1[r]->n21);
            s01 += (v1[r]->n01);
            s0 += (v1[r]->n0);
            s2 += v1[r]->n2;
            s210 += (v1[r]->n21)*(v1[r]->n0);
            s012 += (v1[r]->n01)*(v1[r]->n2);
            s02 += (v1[r]->n0)*(v1[r]->n2);
        }
        ans += (s21*s0-s210+s01*s2-s012);
        if (Fn[0]==0) {
            ans += s21;
        } else if (Fn[0]==1) {
            ans += (s0*s2-s02);
        } else {
            ans += s01;
        }
    }
    void upd(ll x, ll vf) {
        if (x==0) {
            ll v0 = Fn[0];
            if (v0==0) {
                ans -= s21;
            } else if (v0==1) {
                ans -= (s0*s2-s02);
            } else {
                assert(v0==2);
                ans -= s01;
            }
            if (vf==0) {
                ans += s21;
            } else if (vf==1) {
                ans += (s0*s2-s02);
            } else {
                assert(vf==2);
                ans += s01;
            }
        } else {
            ll v0 = Fn[0];
            if (v0==0) {
                ans -= s21;
            } else if (v0==1) {
                ans -= (s0*s2-s02);
            } else {
                assert(v0==2);
                ans -= s01;
            }
            ans -= (s21*s0-s210+s01*s2-s012);

            ll i = strl[x].first;
            s21 -= (v1[i]->n21);
            s01 -= (v1[i]->n01);
            s2 -= (v1[i]->n2);
            s0 -= (v1[i]->n0);
            s210 -= (v1[i]->n21)*(v1[i]->n0);
            s012 -= (v1[i]->n01)*(v1[i]->n2);
            s02 -= (v1[i]->n0)*(v1[i]->n2);

            (*v1[i]).upd(strl[x].second,vf);

            i = strl[x].first;
            s21 += (v1[i]->n21);
            s01 += (v1[i]->n01);
            s2 += (v1[i]->n2);
            s0 += (v1[i]->n0);
            s210 += (v1[i]->n21)*(v1[i]->n0);
            s012 += (v1[i]->n01)*(v1[i]->n2);
            s02 += (v1[i]->n0)*(v1[i]->n2);

            v0 = Fn[0];
            if (v0==0) {
                ans += s21;
            } else if (v0==1) {
                ans += (s0*s2-s02);
            } else {
                assert(v0==2);
                ans += s01;
            }
            ans += (s21*s0-s210+s01*s2-s012);
        }
        Fn[x]=vf;
    }
};

vector<ll> adj[Nm];
bool found[Nm];
ll sz[Nm]; 
ll rev[Nm];
vector<cdt*> cdtr;

ll getsz(ll x, ll pr = -1) {
    sz[x]=1;
    for (ll y: adj[x]) {
        if (y != pr && !found[y]) {
            sz[x]+=getsz(y,x);
        }
    }
    return sz[x];
}

ll getctr(ll x, ll sz0, ll pr=-1) {
    for (ll y: adj[x]) {
        if (y != pr && !found[y]) {
            if (2*sz[y]>=sz0) {
                return getctr(y,sz0,x);
            }
        }
    }
    return x;
}

ll dind = 0; //index in cdtr

void bldDcmp(ll x=0) { //start, previous
    ll sz0 = getsz(x);
    ll y = getctr(x,sz0);
    vector<vector<ll>> nadj; //new adjacency
    vector<ll> fnew;
    ll M = 0;
    queue<pii> q0;
    q0.push({y,-1});
    while (!q0.empty()) {
        pii p0 = q0.front(); q0.pop();
        ll z = p0.first; ll pz = p0.second;
        rlbl[z]=M++;
        nadj.push_back((vector<ll>){});
        fnew.push_back(F[z]);
        locs[z].push_back({dind,rlbl[z]});
        if (pz != -1) {
            nadj[rlbl[z]].push_back(rlbl[pz]);
            nadj[rlbl[pz]].push_back(rlbl[z]);
        }
        for (ll zn: adj[z]) {
            if (!found[zn] && zn != pz) {
                q0.push({zn,z});
            }
        }
    }
    cdtr.push_back(new cdt(M,nadj,fnew));
    found[y]=1;
    dind++;
    for (ll z: adj[y]) {
        if (!found[z]) {
            bldDcmp(z);
        }
    }
}

void init(int N1, vector<int> F1, vector<int> U1, vector<int> V1, int Q) {
    N=N1;
    F=F1;
    U=U1;
    V=V1;
    for (ll i=0;i<(N-1);i++) {
        adj[U[i]].push_back(V[i]);
        adj[V[i]].push_back(U[i]);
    }
    bldDcmp(); //build centroid decomposition
}

void change(int x, int y) {
    for (pii p0: locs[x]) {
        (*cdtr[p0.first]).upd(p0.second,y);
    }
}

long long num_tours() {
    return ans;
}

In file included from /usr/include/c++/13/vector:63,
                 from joitour.h:1,
                 from answer.code:3:
/usr/include/c++/13/bits/allocator.h: In destructor ‘std::_Bvector_base<std::allocator<bool> >::_Bvector_impl::~_Bvector_impl()’:
/usr/include/c++/13/bits/allocator.h:184:7: error: inlining failed in call to ‘always_inline’ ‘std::allocator< <template-parameter-1-1> >::~allocator() noexcept [with _Tp = long unsigned int]’: target specific option mismatch
  184 |       ~allocator() _GLIBCXX_NOTHROW { }
      |       ^
In file included from /usr/include/c++/13/vector:67:
/usr/include/c++/13/bits/stl_bvector.h:557:14: note: called from here
  557 |       struct _Bvector_impl
      |              ^~~~~~~~~~~~~