#include using namespace std; typedef long long ll; typedef long double ld; #define inf 1000000007 #define MP make_pair #define MT make_tuple #define PB push_back #define fi first #define se second #define rep(i,n) for(int i = 0; i < (int)(n); ++i) #define rrep(i,n) for(int i = (int)n-1; i >= 0; --i) #define srep(i,a,b) for(int i = (int)a; i < (int)(b); ++i) #define all(x) (x).begin(),(x).end() #define SUM(v) accumulate(all(v), 0LL) #define MIN(v) *min_element(all(v)) #define MAX(v) *max_element(all(v)) #define lb(c, x) distance((c).begin(), lower_bound(all(c), (x))) #define ub(c, x) distance((c).begin(), upper_bound(all(c), (x))) #define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()) #define SZ(c) (int)(c).size() template ostream& operator << (ostream& os, vector& vec) { os << "{"; for (int i = 0; i<(int)vec.size(); i++) { os << vec[i] << (i + 1 == (int)vec.size() ? "" : ", "); } os << "}"; return os; } // pair出力 template ostream& operator << (ostream& os, pair pair_var) { os << "(" << pair_var.first << ", " << pair_var.second << ")"; return os; } // map出力 template ostream& operator << (ostream& os, map& map_var) { os << "{"; for(auto itr = map_var.begin(); itr != map_var.end(); itr++){ os << "(" << itr->first << ", " << itr->second << ")"; itr++; if(itr != map_var.end()) os << ", "; itr--; } os << "}"; return os; } // set 出力 template ostream& operator << (ostream& os, set& set_var) { os << "{"; for(auto itr = set_var.begin(); itr != set_var.end(); itr++){ os << (*itr); ++itr; if(itr != set_var.end()) os << ", "; itr--; } os << "}"; return os; } // tuple 出力 template void out(ostream &os,const Tuple &t){} template void out(ostream &os,const Tuple &t){ if(N)os<<", "; os<(t); out(os,t); } template ostream& operator<<(ostream &os, const tuple &t){ os<<"("; out<0,tuple,Ts...>(os,t); os<<")"; return os; } #define overload2(_1, _2, name, ...) name #define vec(type, name, ...) vector name(__VA_ARGS__) #define VEC(type, name, size) \ vector name(size); \ IN(name) #define vv(type, name, h, ...) vector> name(h, vector(__VA_ARGS__)) #define VV(type, name, h, w) \ vector> name(h, vector(w)); \ IN(name) #define vvv(type, name, h, w, ...) vector>> name(h, vector>(w, vector(__VA_ARGS__))) #define vvvv(type, name, a, b, c, ...) \ vector>>> name(a, vector>>(b, vector>(c, vector(__VA_ARGS__)))) #define INT(...) \ int __VA_ARGS__; \ IN(__VA_ARGS__) #define LL(...) \ ll __VA_ARGS__; \ IN(__VA_ARGS__) #define STR(...) \ string __VA_ARGS__; \ IN(__VA_ARGS__) #define CHR(...) \ char __VA_ARGS__; \ IN(__VA_ARGS__) #define DBL(...) \ double __VA_ARGS__; \ IN(__VA_ARGS__) int scan() { return getchar(); } void scan(int &a) { cin >> a; } void scan(long long &a) { cin >> a; } void scan(char &a) { cin >> a; } void scan(double &a) { cin >> a; } void scan(string &a) { cin >> a; } template void scan(pair &p) { scan(p.first), scan(p.second); } template void scan(vector &); template void scan(vector &a) { for(auto &i : a) scan(i); } template void scan(T &a) { cin >> a; } void IN() {} template void IN(Head &head, Tail &...tail) { scan(head); IN(tail...); } const string YESNO[2] = {"NO", "YES"}; const string YesNo[2] = {"No", "Yes"}; const string yesno[2] = {"no", "yes"}; void YES(bool t = 1) { cout << YESNO[t] << endl; } void NO(bool t = 1) { YES(!t); } void Yes(bool t = 1) { cout << YesNo[t] << endl; } void No(bool t = 1) { Yes(!t); } void yes(bool t = 1) { cout << yesno[t] << endl; } void no(bool t = 1) { yes(!t); } #ifdef LOCAL void debug_out() { cerr << endl; } template void debug_out(Head H, Tail... T) { cerr << " " << H; debug_out(T...); } #define dbg(...) \ cerr << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__) #define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl #else #define dbg(...) (void(0)) #define dump(x) (void(0)) #endif template std::enable_if_t::value> fill(A& array, const T& val) { array = val; } template std::enable_if_t::value> fill(A& array, const T& val) { for (auto& a : array) { fill(a, val); } } template T ceil(T x, S y) { assert(y); return (y < 0 ? ceil(-x, -y) : (x > 0 ? (x + y - 1) / y : x / y)); } template T floor(T x, S y) { assert(y); return (y < 0 ? floor(-x, -y) : (x > 0 ? x / y : x / y - (x % y == 0 ? 0 : 1))); } vector iota(int n) {vector a(n);iota(all(a), 0);return a;} template T POW(T x, int n) {T res = 1;for(; n; n >>= 1, x *= x){if(n & 1) res *= x;}return res;} ll pow2(int i) { return 1LL << i; } int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); } int topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); } int lowbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); } int lowbit(ll a) { return a == 0 ? 64 : __builtin_ctzll(a); } // int allbit(int n) { return (1 << n) - 1; } ll allbit(ll n) { return (1LL << n) - 1; } int popcount(signed t) { return __builtin_popcount(t); } int popcount(ll t) { return __builtin_popcountll(t); } bool ispow2(int i) { return i && (i & -i) == i; } template void fold_in(vector &v) {} template void fold_in(vector &v, Head &&a, Tail &&...tail) { for(auto e : a) v.emplace_back(e); fold_in(v, tail...); } template void renumber(vector &v) {} template void renumber(vector &v, Head &&a, Tail &&...tail) { for(auto &&e : a) e = lb(v, e); renumber(v, tail...); } template void zip(vector &head, Args &&...args) { vector v; fold_in(v, head, args...); sort(all(v)), v.erase(unique(all(v)), v.end()); renumber(v, head, args...); } template inline bool chmax(T &a, T b){ if(a inline bool chmin(T &a, T b){ if(a>b){ a = b; return true; } return false; } template class BIT { private: int n; vector bit; public: // 0_indexed で i 番目の要素に x を加える void add(int i, T x){ i++; while(i < n){ bit[i] += x, i += i & -i; } } // 0_indexed で [0,i] の要素の和(両閉区間!!) T sum(int i){ i++; T s = 0; while(i > 0){ s += bit[i], i -= i & -i; } return s; } BIT(){} //初期値がすべて0の場合 BIT(int sz) : n(sz+1), bit(n, 0){} BIT(const vector& v) : n((int)v.size()+1), bit(n, 0){ for(int i = 0; i < n-1; i++){ add(i,v[i]); } } void print(){ for(int i = 0; i < n-1; i++){ cout< inv(n); rep(i,n)a[i]--; rep(i,n)inv[a[i]] = i; BIT bit(n+1); rep(i,n){ bit.add(i,1); } vector flag(n); for(int i=n-1;i>=0;i--){ if(bit.sum(inv[i])%2==1){ flag[i] = 1; }else{ flag[i] = 0; } bit.add(inv[i],-1); } rep(i,n)bit.add(i,1); int id = n-1; int pre = n; vector > res; bool ng = 0; while(1){ dbg(flag); dbg(res); dbg(inv); // bit.print(); while(id!=0&&flag[id])id--; if(id==0){ for(int i=pre-1;i>=id;i--){ if(bit.sum(inv[i])%2==0){ ng = 1; break; }else{ res.push_back(MP(i,bit.sum(inv[i]))); bit.add(inv[i],-1); } } break; } while(id!=0&&flag[id-1]==0){ id--; } dbg(id,bit.sum(inv[id])); while(bit.sum(inv[id])%2==0){ if(bit.sum(inv[pre-1])%2==1){ res.push_back({pre-1,bit.sum(inv[pre-1])}); bit.add(inv[pre-1],-1); pre--; }else{ ng = 1; break; } } dbg(res); if(ng)break; dbg(res); dbg(pre,id); if(bit.sum(inv[id])%2==1){ res.push_back({id,bit.sum(inv[id])}); bit.add(inv[id],-1); for(int i = pre-1;i>id;i--){ if(bit.sum(inv[i])%2==0){ ng = 1; break; }else{ res.push_back(MP(i,bit.sum(inv[i]))); bit.add(inv[i],-1); } } pre = id; id--; }else{ ng = 1; } if(ng)break; } if(ng){ No(); return 0; } Yes(); reverse(all(res)); for(auto [x,y]:res){ cout << x+1 << " " << y << "\n"; } return 0; }