Problem: Grigory loves strings. Recently he found a metal strip on a loft. The strip had length n and consisted of letters "V" and "K". Unfortunately, rust has eaten some of the letters so that it's now impossible to understand which letter was written.

Grigory couldn't understand for a long time what these letters remind him of, so he became interested in the following question: if we put a letter "V" or "K" on each unreadable position, which values can the period of the resulting string be equal to?

A period of a string is such an integer d from 1 to the length of the string that if we put the string shifted by d positions to the right on itself, then all overlapping letters coincide. For example, 3 and 5 are periods of "VKKVK".

Input

There are several (at least one) test cases in the input. The first line contains single integer — the number of test cases.

There is an empty line before each test case. Each test case is described in two lines: the first line contains single integer n (1 ≤ n ≤ 5·105) — the length of the string, the second line contains the string of length n, consisting of letters "V", "K" and characters "?". The latter means the letter on its position is unreadable.

It is guaranteed that the sum of lengths among all test cases doesn't exceed 5·105.

For hacks you can only use tests with one test case.

Output

For each test case print two lines. In the first line print the number of possible periods after we replace each unreadable letter with "V" or "K". In the next line print all these values in increasing order.

Example

Input

3
 
5
V??VK
 
6
??????
 
4
?VK?


Output

2
3 5
6
1 2 3 4 5 6
3
2 3 4

Note

In the first test case from example we can obtain, for example, "VKKVK", which has periods 3 and 5.

In the second test case we can obtain "VVVVVV" which has all periods from 1 to 6.

In the third test case string "KVKV" has periods 2 and 4, and string "KVKK" has periods 3 and 4.

Solution (in CPP):

Solution:
#pragma comment(linker, "/stack:20000000")
#pragma GCC optimize("Ofast")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx")

#define _CRT_SECURE_NO_WARNINGS
# include <iostream>
# include <cmath>
# include <algorithm>
# include <stdio.h>
# include <cstdint>
# include <cstring>
# include <string>
# include <cstdlib>
# include <vector>
# include <bitset>
# include <map>
# include <queue>
# include <ctime>
# include <stack>
# include <set>
# include <list>
# include <random>
# include <deque>
# include <functional>
# include <iomanip>
# include <sstream>
# include <fstream>
# include <complex>
# include <numeric>
# include <immintrin.h>
# include <cassert>
# include <array>
# include <tuple>

using namespace std;

// Let's define unordered map
# ifdef __GNUC__
# if __cplusplus > 199711L
# include <unordered_set>
# include <unordered_map>
# else
# include <tr1/unordered_map>
# include <tr1/unordered_set>
using namespace tr1;
# endif
# else
# include <unordered_map>
# include <unordered_set>
# endif

#define VA_NUM_ARGS(...) VA_NUM_ARGS_IMPL_((0,__VA_ARGS__, 6,5,4,3,2,1))
#define VA_NUM_ARGS_IMPL_(tuple) VA_NUM_ARGS_IMPL tuple
#define VA_NUM_ARGS_IMPL(_0,_1,_2,_3,_4,_5,_6,N,...) N
#define macro_dispatcher(macro, ...) macro_dispatcher_(macro, VA_NUM_ARGS(__VA_ARGS__))
#define macro_dispatcher_(macro, nargs) macro_dispatcher__(macro, nargs)
#define macro_dispatcher__(macro, nargs) macro_dispatcher___(macro, nargs)
#define macro_dispatcher___(macro, nargs) macro ## nargs
#define DBN1(a)           cerr<<#a<<"="<<(a)<<"\n"
#define DBN2(a,b)         cerr<<#a<<"="<<(a)<<", "<<#b<<"="<<(b)<<"\n"
#define DBN3(a,b,c)       cerr<<#a<<"="<<(a)<<", "<<#b<<"="<<(b)<<", "<<#c<<"="<<(c)<<"\n"
#define DBN4(a,b,c,d)     cerr<<#a<<"="<<(a)<<", "<<#b<<"="<<(b)<<", "<<#c<<"="<<(c)<<", "<<#d<<"="<<(d)<<"\n"
#define DBN5(a,b,c,d,e)   cerr<<#a<<"="<<(a)<<", "<<#b<<"="<<(b)<<", "<<#c<<"="<<(c)<<", "<<#d<<"="<<(d)<<", "<<#e<<"="<<(e)<<"\n"
#define DBN6(a,b,c,d,e,f) cerr<<#a<<"="<<(a)<<", "<<#b<<"="<<(b)<<", "<<#c<<"="<<(c)<<", "<<#d<<"="<<(d)<<", "<<#e<<"="<<(e)<<", "<<#f<<"="<<(f)<<"\n"
#define DBN(...) macro_dispatcher(DBN, __VA_ARGS__)(__VA_ARGS__)
#define DA(a,n) cerr<<#a<<"=["; printarray(a,n); cerr<<"]\n"
#define DAR(a,n,s) cerr<<#a<<"["<<s<<"-"<<n-1<<"]=["; printarray(a,n,s); cerr<<"]\n"

#ifdef _MSC_VER
#define PREFETCH(ptr, rw, level) ((void)0)
#else
#define PREFETCH(ptr, rw, level) __builtin_prefetch(ptr, rw, level)
#endif

#ifdef LOCAL
#define CURTIME() cerr << clock() * 1.0 / CLOCKS_PER_SEC << endl
#else
#define CURTIME()
#endif

#define mp make_pair
typedef long long ll;
typedef unsigned int uint;
typedef unsigned long long ull;
typedef pair<int, int> pii;
typedef pair<long long, long long> pll;
typedef vector<int> vi;
typedef vector<long long> vll;
typedef int itn;

template<class T1, class T2, class T3>
struct triple{ T1 a; T2 b; T3 c; triple() : a(T1()), b(T2()), c(T3()) {}; triple(T1 _a, T2 _b, T3 _c) :a(_a), b(_b), c(_c){} };
template<class T1, class T2, class T3>
bool operator<(const triple<T1,T2,T3>&t1,const triple<T1,T2,T3>&t2){if(t1.a!=t2.a)return t1.a<t2.a;else if(t1.b!=t2.b)return t1.b<t2.b;else return t1.c<t2.c;}
template<class T1, class T2, class T3>
bool operator>(const triple<T1,T2,T3>&t1,const triple<T1,T2,T3>&t2){if(t1.a!=t2.a)return t1.a>t2.a;else if(t1.b!=t2.b)return t1.b>t2.b;else return t1.c>t2.c;}
#define tri triple<int,int,int>
#define trll triple<ll,ll,ll>

#define FI(n) for(int i=0;i<(n);++i)
#define FJ(n) for(int j=0;j<(n);++j)
#define FK(n) for(int k=0;k<(n);++k)
#define FL(n) for(int l=0;l<(n);++l)
#define FQ(n) for(int q=0;q<(n);++q)
#define FOR(i,a,b) for(int i = (a), __e = (int) (b); i < __e; ++i)
#define all(a) std::begin(a), std::end(a)
#define reunique(v) v.resize(unique(v.begin(), v.end()) - v.begin())

#define sqr(x) ((x) * (x))
#define sqrt(x) sqrt(1.0 * (x))
#define pow(x, n) pow(1.0 * (x), n)

#define COMPARE(obj) [&](const std::decay<decltype(obj)>::type& a, const std::decay<decltype(obj)>::type& b)
#define COMPARE_BY(obj, field) [&](const std::decay<decltype(obj)>::type& a, const std::decay<decltype(obj)>::type& b) { return a.field < b.field; }

#define checkbit(n, b) (((n) >> (b)) & 1)
#define setbit(n, b) ((n) | (static_cast<std::decay_t<decltype(n)>>(1) << (b)))
#define removebit(n, b) ((n) & ~(static_cast<std::decay_t<decltype(n)>>(1) << (b)))
#define flipbit(n, b) ((n) ^ (static_cast<std::decay_t<decltype(n)>>(1) << (b)))
inline int countBits(uint v){v=v-((v>>1)&0x55555555);v=(v&0x33333333)+((v>>2)&0x33333333);return((v+(v>>4)&0xF0F0F0F)*0x1010101)>>24;}
inline int countBits(ull v){uint t=v>>32;uint p=(v & ((1ULL << 32) - 1)); return countBits(t) + countBits(p); }
inline int countBits(ll v){return countBits((ull)v); }
inline int countBits(int v){return countBits((uint)v); }
unsigned int reverseBits(uint x){ x = (((x & 0xaaaaaaaa) >> 1) | ((x & 0x55555555) << 1)); x = (((x & 0xcccccccc) >> 2) | ((x & 0x33333333) << 2)); x = (((x & 0xf0f0f0f0) >> 4) | ((x & 0x0f0f0f0f) << 4)); x = (((x & 0xff00ff00) >> 8) | ((x & 0x00ff00ff) << 8)); return((x >> 16) | (x << 16)); }
template<class T> inline int sign(T x){ return x > 0 ? 1 : x < 0 ? -1 : 0; }
inline bool isPowerOfTwo(int x){ return (x != 0 && (x&(x - 1)) == 0); }
template<class T1, class T2, class T3> T1 inline clamp(T1 x, const T2& a, const T3& b) { if (x < a) return a; else if (x > b) return b; else return x; }
unsigned long long rdtsc() { unsigned long long ret = 0;
#ifdef __clang__
    return __builtin_readcyclecounter();
#endif
#ifndef _MSC_VER
    asm volatile("rdtsc" : "=A" (ret) : :);
#endif
    return ret; }
// Fast IO ********************************************************************************************************
const int __BS = 4096;
static char __bur[__BS + 16], *__er = __bur + __BS, *__ir = __er;
template<class T = int> T read_int() {
    auto c = [&]() { if (__ir == __er) memset(__bur, 0, __BS), cin.read(__bur, __BS), __ir = __bur; };
    c(); while (*__ir && (*__ir < '0' || *__ir > '9') && *__ir != '-') ++__ir; c();
    bool m = false; if (*__ir == '-') ++__ir, c(), m = true;
    T r = 0; while (*__ir >= '0' && *__ir <= '9') r = r * 10 + *__ir - '0', ++__ir, c();
    ++__ir; return m ? -r : r;
}
static char __buw[__BS + 20], *__iw = __buw, *__ew = __buw + __BS;
template<class T>
void write_int(T x, char endc = '\n') {
    if (x < 0) *__iw++ = '-', x = -x; if (x == 0) *__iw++ = '0';
    char* s = __iw;
    while (x) { T t = x / 10; char c = x - 10 * t + '0'; *__iw++ = c; x = t; }
    char* f = __iw - 1; while (s < f) swap(*s, *f), ++s, --f;
    if (__iw > __ew) cout.write(__buw, __iw - __buw), __iw = __buw;
    *__iw++ = endc;
}
struct __FL__ { ~__FL__() { if (__iw != __buw) cout.write(__buw, __iw - __buw); } };
static __FL__ __flushVar__;

//STL output *****************************************************************************************************
#define TT1 template<class T>
#define TT1T2 template<class T1, class T2>
#define TT1T2T3 template<class T1, class T2, class T3>
TT1T2 ostream& operator << (ostream& os, const pair<T1, T2>& p);
TT1 ostream& operator << (ostream& os, const vector<T>& v);
TT1T2 ostream& operator << (ostream& os, const set<T1, T2>&v);
TT1T2 ostream& operator << (ostream& os, const multiset<T1, T2>&v);
TT1T2 ostream& operator << (ostream& os, priority_queue<T1, T2> v);
TT1T2T3 ostream& operator << (ostream& os, const map<T1, T2, T3>& v);
TT1T2T3 ostream& operator << (ostream& os, const multimap<T1, T2, T3>& v);
TT1T2T3 ostream& operator << (ostream& os, const triple<T1, T2, T3>& t);
template<class T, size_t N> ostream& operator << (ostream& os, const array<T, N>& v);
TT1T2 ostream& operator << (ostream& os, const pair<T1, T2>& p){ return os <<"("<<p.first<<", "<< p.second<<")"; }
TT1 ostream& operator << (ostream& os, const vector<T>& v){       bool f=1;os<<"[";for(auto& i : v) { if (!f)os << ", ";os<<i;f=0;}return os << "]"; }
template<class T, size_t N> ostream& operator << (ostream& os, const array<T, N>& v) {     bool f=1;os<<"[";for(auto& i : v) { if (!f)os << ", ";os<<i;f=0;}return os << "]"; }
TT1T2 ostream& operator << (ostream& os, const set<T1, T2>&v){    bool f=1;os<<"[";for(auto& i : v) { if (!f)os << ", ";os<<i;f=0;}return os << "]"; }
TT1T2 ostream& operator << (ostream& os, const multiset<T1,T2>&v){bool f=1;os<<"[";for(auto& i : v) { if (!f)os << ", ";os<<i;f=0;}return os << "]"; }
TT1T2T3 ostream& operator << (ostream& os, const map<T1,T2,T3>& v){ bool f = 1; os << "["; for (auto& ii : v) { if (!f)os << ", "; os << "(" << ii.first << " -> " << ii.second << ") "; f = 0; }return os << "]"; }
TT1T2 ostream& operator << (ostream& os, const multimap<T1, T2>& v){ bool f = 1; os << "["; for (auto& ii : v) { if (!f)os << ", "; os << "(" << ii.first << " -> " << ii.second << ") "; f = 0; }return os << "]"; }
TT1T2 ostream& operator << (ostream& os, priority_queue<T1, T2> v) { bool f = 1; os << "["; while (!v.empty()) { auto x = v.top(); v.pop(); if (!f) os << ", "; f = 0; os << x; } return os << "]"; }
TT1T2T3 ostream& operator << (ostream& os, const triple<T1, T2, T3>& t){ return os << "(" << t.a << ", " << t.b << ", " << t.c << ")"; }
TT1T2 void printarray(const T1& a, T2 sz, T2 beg = 0){ for (T2 i = beg; i<sz; i++) cout << a[i] << " "; cout << endl; }

//STL input *****************************************************************************************************
TT1T2T3 inline istream& operator >> (istream& os, triple<T1, T2, T3>& t);
TT1T2 inline istream& operator >> (istream& os, pair<T1, T2>& p) { return os >> p.first >> p.second; }
TT1 inline istream& operator >> (istream& os, vector<T>& v) {
    if (v.size()) for (T& t : v) os >> t; else {
        string s; T obj; while (s.empty()) {getline(os, s); if (!os) return os;}
        stringstream ss(s); while (ss >> obj) v.push_back(obj);
    }
    return os;
}
TT1T2T3 inline istream& operator >> (istream& os, triple<T1, T2, T3>& t) { return os >> t.a >> t.b >> t.c; }

//Pair magic *****************************************************************************************************
#define PT1T2 pair<T1, T2>
TT1T2 inline PT1T2 operator+(const PT1T2 &p1 , const PT1T2 &p2) { return PT1T2(p1.first + p2.first, p1.second + p2.second); }
TT1T2 inline PT1T2& operator+=(PT1T2 &p1 , const PT1T2 &p2) { p1.first += p2.first, p1.second += p2.second; return p1; }
TT1T2 inline PT1T2 operator-(const PT1T2 &p1 , const PT1T2 &p2) { return PT1T2(p1.first - p2.first, p1.second - p2.second); }
TT1T2 inline PT1T2& operator-=(PT1T2 &p1 , const PT1T2 &p2) { p1.first -= p2.first, p1.second -= p2.second; return p1; }

#undef TT1
#undef TT1T2
#undef TT1T2T3

#define FREIN(FILE) freopen(FILE, "rt", stdin)
#define FREOUT(FILE) freopen(FILE, "wt", stdout)
#ifdef LOCAL
#define BEGIN_PROFILE(idx, name) int profileIdx = idx; profileName[profileIdx] = name; totalTime[profileIdx] -= rdtsc() / 1e3;
#define END_PROFILE totalTime[profileIdx] += rdtsc() / 1e3; totalCount[profileIdx]++;
#else
#define BEGIN_PROFILE(idx, name)
#define END_PROFILE
#endif

template<class T> inline void normmod(T &x, T m) { x %= m; if (x < 0) x += m; }
template<class T1, class T2> inline T2 summodfast(T1 x, T1 y, T2 m) { T2 res = x + y; if (res >= m) res -= m; return res; }
template<class T1, class T2, class T3> inline void addmodfast(T1 &x, T2 y, T3 m) { x += y; if (x >= m) x -= m; }
template<class T1, class T2, class T3> inline void submodfast(T1 &x, T2 y, T3 m) { x -= y; if (x < 0) x += m; }
#if INTPTR_MAX == INT32_MAX or !defined(__SIZEOF_INT128__)
inline ll mulmod(ll x, ll n, ll m){ ll r = 0; normmod(x, m); normmod(n, m); while (n) { if (n & 1) r += x; x += x; if (r >= m) r -= m; if (x >= m) x -= m; n /= 2; } return r; }
#else
using int128 = __int128;
inline ll mulmod(ll x, ll n, ll m){ return __int128(x) * n % m; }
#endif
inline ll powmod(ll x, ll n, ll m){ ll r = 1; normmod(x, m); while (n){ if (n & 1)r = (r*x) % m; x = (x*x) % m; n /= 2; }return r; }
inline ll powmulmod(ll x, ll n, ll m) { ll res = 1; normmod(x, m); while (n){ if (n & 1)res = mulmod(res, x, m); x = mulmod(x, x, m); n /= 2; } return res; }
template<class T> inline T gcd(T a, T b) { while (b) { a %= b; T t = a; a = b; b = t; } return a; }
inline ll lcm(ll a, ll b){ return a / gcd(a, b) * b; }
template<class T> inline T gcd(T a, T b, T c){ return gcd(gcd(a, b), c); }
ll gcdex(ll a, ll b, ll& x, ll& y) {
    if (!a) { x = 0; y = 1; return b; }
    ll y1; ll d = gcdex(b % a, a, y, y1); x = y1 - (b / a) * y;
    return d;
}
template<class T> bool isPrime(T x) { if (x <= 4 || x % 2 == 0 || x % 3 == 0) return x == 2 || x == 3;
    for (T i = 5; i * i <= x; i += 6) if (x % i == 0 || x % (i + 2) == 0) return 0; return 1; }
bool millerRabin(long long n) {
    if (n <= 1000) return isPrime(n);
    long long s = n - 1; int t = 0; while (s % 2 == 0) s /= 2, ++t;
    for (int a : {2, 325, 9375, 28178, 450775, 9780504, 1795265022}) { if (!(a %= n)) return true;
        long long f = powmulmod(a, s, n); if (f == 1 || f == n - 1) continue;
        for (int i = 1; i < t; ++i) if ((f = mulmod(f, f, n)) == n - 1) goto nextp;
        return false; nextp:;
    } return true;
}

// Useful constants

//int some_primes[7] = {24443, 100271, 1000003, 1000333, 5000321, 98765431, 1000000123};
#define T9          1000000000
#define T18         1000000000000000000LL
#define INF         1011111111
#define LLINF       1000111000111000111LL
#define mod         1000000007
#define EPS         (double)1e-10
#define PI          3.14159265358979323846264
#define link        asaxlajrewqwe
#define rank        wahayawehasdakw
//*************************************************************************************

int32_t solve();
int32_t main(int argc, char** argv) {
    ios_base::sync_with_stdio(0);cin.tie(0);
#ifdef LOCAL
//            FREIN("input.txt");
    //        FREOUT("out.txt");
#endif
    return solve();
}

//using cd = complex<double>;
using cd = pair<double, double>;
cd foo(int x) {
    return {x, 0};
}
cd foo(cd x) {
    return x;
}
cd operator*(const cd& c1, const cd& c2) {
    return {c1.first * c2.first - c1.second * c2.second, c1.first * c2.second + c1.second * c2.first};
}
cd w[1 << 21];
template<class T>
void fft(T x, cd* y, int n, int k = 1) {
    if (n == 1) {
        y[0] = foo(x[0]);
    } else {
        n /= 2;
        fft(x, y, n, k * 2);
        fft(x + k, y + n, n, k * 2);
        for (int i = 0, j = 0; i < n; i++, j += k) {
            auto q = y[i + n] * w[j];
            y[i + n] = y[i] - q;
            y[i] += q;
        }
    }
}

template<ll x, int power> struct ConstPower;
template<ll x> struct ConstPower<x, 0> { static constexpr ll value = 1LL; };
template<ll x, int power> struct ConstPower { static constexpr ll value = ConstPower<x, power - 1>::value * x; };
#define POWER(X, Y) ConstPower<X, Y>::value
constexpr int K = 2;
constexpr int T = POWER(10, K);
vector<int> mul(vector<int> a, vector<int> b) {
    int n = int(a.size() + b.size());
    while (n & (n - 1)) {
        ++n;
    }
    a.resize(n);
    b.resize(n);
    for (int i = 0; i < n; ++i) {
        auto s = polar(1.0, i * 2 * PI / n);
        w[i] = {s.real(), s.imag()};
    }
    vector<cd> x(n);
    vector<cd> y(n);
    fft(a.data(), x.data(), n);
    fft(b.data(), y.data(), n);
    FI(n) {
        x[i] = x[i] * y[i];
    }
    FI(n) {
        w[i].second = -w[i].second;
    }
    fft(x.data(), y.data(), n);
    FI(n) {
        a[i] = (y[i].first / n) + 0.5;
    }
    return a;
}
bool good[501010];
int solve() {
    int tc;
    cin >> tc;
    while (tc--) {
        int n;
        cin >> n;
        string s;
        getline(cin, s);
        getline(cin, s);
        vector<int> a(n);
        vector<int> b(n);
        FI(n) {
            a[i] = (s[i] == 'V');
        }
        FI(n) {
            b[i] = (s[i] == 'K');
        }
        reverse(all(b));
        auto res = mul(a, b);
        for (int i = 1; i <= n; ++i) {
            good[i] = true;
        }
        vector<int> ans = {n};
        for (int i = n - 1; i > 0; --i) {
            for (int j = i + i; j <= n; j += i) {
                if (!good[j]) {
                    good[i] = false;
                    break;
                }
            }
            if (good[i]) {
                int r = n - 1;
                if (res[r + i] + res[r - i]) {
                    good[i] = false;
                } else {
                    ans.push_back(i);
                }
            }
        }
        reverse(all(ans));
        write_int(ans.size());
        for (int x : ans) {
            write_int(x, ' ');
        }
    }
    
    return 0;
}